GEODESIC PROGRAM MANUAL ;note: this manual is available from within the program itself under HELP. CONTENTS (use drop-downs to select) INTRODUCTION... data on geodesics, program theory, and author's notes GETTING STARTED... system requirements, set-up, and program limits SCREEN DISPLAY... detailed information on screen displayed spheres DROP-DOWN MENUS... using the selections for printing instructions, see FILE, sub catagory Print TOOLBOX... tools and using them CREATING SPHERES... general guide and using your created geodesics Geodesics Geodesic refers to the shortest distance between two points on a sphere (forming a chord), and is always on a great circle (the circle created when a sphere is cut in two exact halves). The concept of creating a sphere using multiple flat faces was expanded by Buckminister Fuller with formulae to convert spherical triangles to flat triangles, as well as other work which aids in creating domes. Unfortunately, the amount of math required to create a geodesic structure is incredibly difficult and tedious. This program is designed to remove the difficulty in generating various spheres and domes. Hopefully, now anybody can create a geodesic structure with no prior mathematical or spherical knowledge. Geodesic dome houses are practical for several reasons. -- First, the inside volume of a sphere is the largest with regard to the surface area. This means that the material required to create the shell is the smallest possible for the inside space. -- Second, the dome is self supporting. No internal construction is necessary to provide roof support. -- Third, the shape of the dome is aero-dynamic. With its smooth round surface, it is less prone to high wind attacks. -- Fourth, it is physically more stable than a standard house. The bulk of the dome is low and there are no large flat walls which can fold flat like a box. It should withstand earthquakes much better. Large domes should not be used in heavy snow conditions since the top of the dome is relatively flat and will allow heavy snow build-up. > Dome House Construction Since domes are constructed using many faces, special consideration needs to be used when sealing the cracks between faces. I believe this to be less troublesome if new techniques are implemented. Three methods come to mind; 1. Melt strips of roofing material such as BRAI (plastic tar) over each crack. 2. Use fiberglass strips or cloth soaked with fiberglass resin over each crack. 3. Use Silicone Rubber in each crack. Large domes with many small faces are weaker than domes made with fewer large faces. This is due to the smaller angles between each face, and can be illustrated by bending a flat piece of paper versus a partially folded piece of paper. The angle of the fold adds strength. Also, when constructing a dome, the full strength is only realized when the dome is completed, and all faces are securely fastened together. Several large domes have collapsed during construction before the final top sections could be installed. This is generally a problem on domes 100 feet or more in diameter. Still, support may be necessary on smaller domes during construction. Usually, the dome should be constructed loosely until all of the faces are in place, then tightened firmly together. This is necessary since small errors in face sizes add up as faces are added around the dome. For instance, if you have a 1/10" error on each face and 50 faces are needed around the base, by the time you arrive at the starting point, you could have a 5" gap or overlap to join up to the first face. This program calculates face construction details. Several selections for wood sizes are available. Framing is generated using perpendicular cuts to the face surface, which means that a miter saw is all that is necessary to cut the frame and studs... no extremely difficult multiple angle cuts. The frames are inset from the outside face edges so they will meet on the inside surface of the dome. This leaves a gap between the outside frames which needs to be filled, and dihedral boards are generated to fill this need. A table saw or radial arm saw is necessary for the strips of dihedral boards outside of the frame, which need to be cut at an angle. These boards provide the pressure strength to support the dome. The alternative to this method of construction is too ugly with multiple compound angle cuts required. Each frame board is provided with bolt hole positions to match adjacent faces. This program also provides outside face dimensions as well as inside face dimensions which are adjusted slightly in size to account for material thickness and dihedral angles (angles between faces). > Program Theory The basic concept of this program is to generate spheres and domes using one of eighteen spherical solids as a starting basis. (All points reside on the sphere surface.) The spherical solid is then broken into smaller triangular faces, and finally cut to provide a flat base. Some of the possibilities are not really practical for creating houses due to the many different face shapes generated, although the this program's method for face construction considerably simplifies otherwise difficult wood cutting. The program maintains two arrays for working with the sphere... a points array and a faces array. The points array stores the cartesian coordinates (x,y,z) of each point. The faces array stores the points used for each face and face attributes. Both these arrays are dynamically altered in size as additional storage becomes necessary. Rotations are performed on the points array only. A change in sphere radius is performed by converting the points to spherical coordinates (vectors... two angles and a length), then altering the length of the vector, and re- converting back to cartesian coordinates. Breakdowns into smaller faces are performed using only two algorithms (methods for performing a task), and all breakdowns are performed with various combinations of the two. 1. The first method is a triacon breakdown which can be used on any face shape. Triacon breakdowns are performed by finding the center of each face and creating a new point above that location on the sphere surface. All of the old face edges go away and new face edges are created between the center points and existing old face points. Effectively, this yields a 1.7 frequency breakdown, and none of the old face edges remain. (A second application of the triacon breakdown restores the old edges with a 3 frequency breakdown product.) 2. The second method is a 2 frequency breakdown which can be used only on triangular faces. A new point is created at the center of each face edge, and new faces are added between the points. Effectively, one triangle is divided into four triangles. Spearpoint raising creates a new point above the center of the face on the sphere surface, then creates new triangles connecting each of the face points. Displaying the sphere on the screen is performed by drawing faces from the back of the sphere to the front so that front faces will will not be hidden by back faces. This was accomplished by calculating the formula for each face plane, then sorting according to the depth of intersection between the plane and the axis line pointing toward you. 3D display for those of you with Stereo-Tek glasses requires that each eye sees an image from a different angle. Two complete pictures are drawn 5 degrees rotation apart. The two pictures are alternately displayed, each eye of the viewer seeing one of the two pictures while the other eye is 'shuttered' off. The effect is a true three dimensional image. The optimum distance from the screen for viewing is about 2 feet. Moving farther away tends to stretch the sphere into an egg shape. Moving closer to the screen flattens the sphere. > Practical Spheres Typically, spheres made using solids of few points (Tetrahedron, Hexahedron) breakdown into faces which have negative dihedral angles (faces which point outward from the sphere and join with other faces in a crevice, or indented joint). These faces have one long edge and two short edges usually. Although this program works properly with these faces, house construction becomes a bit more complex. The most commonly used solids for sphere construction are the Octahedron (8 faces) and the Icosahedron (20 faces). Generally, these shapes breakdown into fewer face shapes since they begin with equalateral triangles only. The Octahedron has a flat base at the half-sphere point. The Icosahedron is usually cut at the 3/8 or 5/8 level. Not only are there fewer face shapes for these spheres, but also the calculations are considerably easier (for those who don't use this program). > Author's Note I began this program with calculation routines to convert between flat and spherical triangles (CALC drop-down menu). It soon became obvious that the difficulty still existed for dome creation. A simpler method was required. Thus the concept of using existing spherical solids as a basis and breaking them down into smaller faces was born. No mathematical knowledge is required by the user... this program provides complex routines for performing the necessary calculations. (I spent considerable time pouring through calculus books and writing routines to solve simultaneous equations, spherical geometry calculations, and other necessary mathematical functions.) The result is an easy to use program which manipulates spherical faces and generates lists with graphical data for the actual construction of a real geodesic structure. I sincerely hope that you enjoy using this program, and possibly get some real benefit from it. If you have any suggestions for improvement or added functions, please let me know. My GEnie BBS address is R.MCKAIG Ray S. McKaig 555 Riverview Drive Boulder Creek, CA 95006 (408) 338-3693 System Requirements You must have a monochrome monitor since this program only runs in high resolution. Also, a hard disk is highly recommended due to the storage size requirements. Although this program will run on a one megabyte machine (spheres are limited by memory available), additional memory is very desirable... four megabytes removes any limitations on the program, or number of faces to be manipulated. > Program Limitations A maximum of 32760 faces is allowed (Far too many from a practical point of view). There is no practical limit to the sphere radius. This program only creates the shell. The interior of the house is left up to the imagination of you. Methodology for sphere breakdown in one case is not as efficient as it could be. The case is equilateral triangles broken into 3 frequency divisions. (frequency is the number of sections each edge of a face is divided into.) It is possible to end up with 2 different triangle shapes only after breakdown, however this program generates three different shapes. The advantage is that the resulting triangles are more uniformly similar in size, yielding a more uniformly spherical sphere. During breakdown, it is important that all faces have adjacent faces touching within the area of where you intend to cut the sphere into a dome. If not, the breakdown algorithm will create additional triangles on the edges having no adjacent faces. (A three frequency breakdown ends up with 4 divisions instead of 3 on the edges.) To prevent this from happening, it is best to start with a full sphere before breakdown. The CAMERA tool is memory intensive. It uses most all of the remaining memory to generate the many picture angles, and the size of the display sphere generated is reduced according to the number of pictures desired and memory available. Please note that saving the movie requires a hard disk due to the size of the file. > Beginning If your disk has a file called GEODESIC.LZH, you will need to decompress the file. This must be done with Quester's LZH decompression program available on BBS systems such as GEnie. HARD DISK: You should create a folder and place all of the files in it. Then you are ready to start. Execute the GEODESIC.PRG file. FLOPPY DISK: Although floppy disks are not recommended due to size limitations, they can be used. This GEODESIC program is self-contained (except for the manual if you intend to access it while in the program). Insert your floppy (a copy, preferably) and execute GEODESIC.PRG. Once this program is executed, you may use a blank floppy disk or one with a manual on it for online help. You can play with the program immediately, but reading the section on TOOLS will most helpful. The next section you should be familiar with are the Drop-Down MENUS. I have always believed that experience is the best teacher, so working (or playing) with the program will give you the experience needed and expertise for most operations. Since this manual is on-line under the HELP drop-down menu, it may be consulted at any time if you find yourself perplexed. Screen Format Upon executing the program, a title picture is displayed while the program initializes and generates the TOOL box display. Once all is initialized, the title picture is rolled up from the bottom of the screen and the main work screen is displayed. The screen has several areas of importance. 1. Across the top line are the drop-down menus, with an area on the top right which gives a short explanation of the TOOL the mouse pointer is over, or if the mouse is to the left of the TOOL box the current tool selection is displayed. 2. On the extreme left, status information about the current sphere is displayed when available. 3. In the center of the screen is the sphere work area, depicted by a circle with cross hairs. 4. Below the circle is the name of the spherical solid currently selected upon which the sphere is based on. 5. Below the circle to the right is the sphere orientation AXIS indicator. It can be changed for X, Y, or Z axis display. 6. Next to the AXIS indicator is a graphical picture of the basic sphere solid with the edge length shown above. The edge length displays the length of all the lines intersecting two faces, which changes with a radius change. This is provided for information only. 7. Above and to the right of the sphere is an area used for status while the program is busy working. 8. The TOOL box is displayed on the right of the screen which houses the working tools and convenience tools. Hot Keys Many of the drop-down menu items provide 'HOT KEY' access for fast selection without using the mouse. On the right of the selection may be a hot key designation tor access. --> '^' indicates the Control key must be pressed prior to the character. --> A 'black box character' indicates that the Alternate key must be pressed prior to the character. --> 'Fn' where n is a number indicates the function key corresponding which is found across the top of the keyboard. > DESK The program version number can be found in the drop-down item 'About GEODESIC'. Loaded desk accessories may be accessed here. > FILE This has the disk operations LOAD, SAVE, DELETE for spheres, the disk MOVIE operations for loading and saving, the disk operation DEGAS for generating DEGAS compatible pictures, and PRINT functions. --> Load Sphere: A previously saved sphere is retrieved from disk --> Save Sphere: The current sphere in the work circle is saved to disk --> Delete Sphere: Allows deleting files on disks. The file type defaults to ".GEO", however any file may be deleted. You are prompted (if the file exists) to insure that you wish to delete the file. --> Load Movie: A previously saved Movie created with the Camera tool is loaded. Note: If your memory available is smaller than when you created the movie, some of the frames will be removed causing jumps in the rotation during display. To avoid this, clear your working sphere first. This can be done by saving the sphere to disk if desired, then selecting a new sphere from the drop-down menu SPHERES. --> Save Movie: You can save a movie to disk which you have generated using the Camera tool. The file is stored in a compressed format on disk. --> Save Degas: This will create a picture of your sphere into a name.PI3 file which can then be painted using the Degas paint program. You can specify the percentage of size you wish for the picture. (The program's title picture was created using this function with various spheres generated.) --> Print: This is a general entry into the various print functions. You may print to the screen, or if you have GDOS installed (from booting) you can print to a graphic printer. A 300 dot-per-inch printer is recommended for construction print-outs. GDOS requires that the ASSIGN.SYS file has an appropriate printer driver for your printer. Picture: You can print a picture of your sphere of varying sizes and display modes. Construction: You can print detailed diagrams for constructing the sphere faces. First, a listing of sphere details, common faces and face numbers to reference them by. Next, graphic printout of face details and orientation dots for each unique face shape is done. Finally, graphic printout of the sphere with face locations and orienting dots is provided. Faces only: Prints the outside surface faces and dimensions only, suitable for paper construction. Faces and Frames: Prints full construction details for house construction. You are first prompted for details on material sizes and number display preference. Note: You may abort printout by pressing the ESC key. (The computer may take a while to finish the current procedure before an abort request is tested) You are then prompted to insure you really wish to abort. When printing to the screen, you may continue to the next screen by pressing any key (except ESC), or the left mouse button. (ESC or the right mouse button will request an abort.) --> Quit exits the program. If you have not saved your sphere since it was modified, you are prompted to do so. Also, if you have used the CAMERA tool and a 'Movie' is in memory, you are asked if you wish to save the movie. (This requires a fair amount of disk space.) > SPHERES Selection of the 18 basic spherical solids for new sphere creations is found here, as well as the desired radius for the sphere. Selecting one of the spheres will clear the workspace and set up the program for a new basic sphere solid creation. If your current sphere has not been saved, you will first be prompted to do so. To generate the new sphere, use the ADD tool in FACE mode (see TOOLS). --> RADIUS The sphere radius can be changed at any time. Click on this selection and type in the new value. Your sphere data will be updated for the new size. > ROTATE Rotation degrees can be set here for the rotation tool (circle with arrows). Several selections for rotation increments are available, the most important have function keys (hot keys) for quick changing. The selections are: .1 Degree 1 Degree 5 Degrees (F5) 10 Degrees (F10) 15 Degrees (F1) 30 Degrees (F3) 45 Degrees (F4) 60 Degrees (F6) 72 Degrees (F7) 90 Degrees (F9) --> Add Face Rotate This is only useful when adding faces to a basic sphere solid, and works with the ADD function in single FACE mode (not AREA mode... these are selected in the tool box). When a new face is joined to another face, the sphere is rotated so the face added is in the front center of the work area. This makes adding multiple faces easier since the sphere need not be manually rotated to a new position to expose an area free for the next face to add. --> SET HOME When this function is selected, the current orientation of the sphere is remembered. At some future time when you have rotated the sphere to a different orientation, you can click on the HOME tool (located in the center of the rotate tool) and have your sphere returned to its home position. > DISPLAY Provides visual display selections. You can reverse the screen, select how you wish to display the sphere, and if you have 3-D glasses connected to the expansion port, you can see the sphere stand out from the screen in its 3-dimensional glory. --> TOGGLE BACKGROUND: Reverses the screen colors --> Show AXIS Toward You: These selections allow the sphere to be viewed from the three different axis. Default is X. X, Y, or Z axis selections are available. Clicking one of these selections re-displays the sphere in a new orientation with the selected axis pointing out of the screen toward you, and changes the AXIS indicator below and to the right of the sphere. --> All Faces: These selections change the sphere display to show all of the sphere faces (as opposed to Front Faces Only). This is useful with solid or shaded faces for displaying spheres with windows or missing sections to see the rear faces, and is also useful with wire-frame mode (All Edges) to see all edges. --> All Edges: Draws all face edges only, no filled faces. This is wire- frame mode, and is probably more useful with 3D glasses since the rear faces appear behind the screen and the front faces stand out toward you. --> Solid Out, Dotted In: Front faces are solid white, while rear faces are pattern filled using the 24 system fill patterns (less black). --> Dotted Out, Solid In: Just the reverse of the above. --> Shaded Faces: 37 shading patterns are used by depth. Front faces are white or lightly shaded while the rear faces become darker... the most rear becoming black. --> Front Faces Only: Only the faces on the front of the sphere are drawn. This is much faster than drawing all of the faces. This is also less confusing when working with the sphere since only the faces you can work on are displayed. The display selections are the same for All Faces (above). Clear Front Faces is wire frame mode... the faces are not filled. --> 3D Stereo-tek Glasses: This is only available if you have the module which came with your glasses plugged into the expansion port of your computer. This activates or deactivates the 3D display capability. > CALC Provides the tedious conversions between spherical and flat triangles for those of you who wish to slug it out the old way of creating Geodesic structures. This is provided as a convenience only for mathematicians working the spherical equations and face breakdowns. --> Spherical from Flat Triangles: Allows entry of flat triangle parameters and calculates the corresponding spherical triangle using the current sphere radius. --> Flat from Spherical Triangles: Allows entry of spherical triangle parameters using the current sphere radius and calculates the corresponding flat triangle. > HELP --> Manual: Online display of this manual --> Operation: A short description for using this program. --> Geodesics: general information on Geodesics Sections The Bottom of the TOOL box has the six basic shapes for creating the basic 18 spherical solids. These are used when first generating a sphere with the ADD tool in FACE mode. Only the appropriate selections are available for the current sphere selected under the SPHERES drop-down menu, as indicated by a white background. Above the basic shapes is section of face work tools. These consist of a mode switch (FACE, AREA) which selects between single face operations or faces within a draw area. The tools in this section are Spearpoint raising, Window toggling, ADD faces, and DELete faces. The next section above has the major modification tools... Frequency Breakdown, and Cut Sphere. Above the major modification tools are the display tools. These consist of sphere rotation tools (circle with arrows), a convenience toggle tool called DISP which switches between display modes, and a toggle tool to switch between a reference circle with cross-hairs or not. The next section up has the Movie tools which allow the generation and display of multiple views of the sphere. > Using FACE or AREA mode --> FACE mode allows single face operations on the four tools in the tool box section (SPEARPOINT, WINDOW, ADD, DEL). Pointing the mouse at the face desired in the sphere working circle and left-clicking activates the function for the tool selected. (Exception: See ADD, FACE mode) --> AREA mode affects the four tools in the tool box section (SPEARPOINT, WINDOW, ADD, DEL). To use, one of the four tools must be selected, and AREA must be selected. Move the mouse into the sphere working circle. Left click the mouse to begin. You can now draw a flashing line around the faces or area you wish to affect. Left clicking again will close the circle and begin the operation selected, else right clicking will abort. > SPEARPOINT This tool raises points in the middle of selected faces and creates new triangles. Each face selected is effectively broken into smaller triangles connected to all points of the face. (See 'Using FACE or AREA mode' for selecting faces) > WINDOW This tool toggles selected faces between 'windows' you can see through, and solid faces. (See 'Using FACE or AREA mode' for selecting faces) > ADD, FACE mode When first creating a basic sphere solid, this tool activates the appropriate basic shapes for the currently selected sphere at the bottom of the tool box. These shapes can be selected by clicking on the shape desired (the shapes not highlighted are available). By moving the mouse into the work screen to the left, the shape appears. When the shape is moved into the sphere circle, the shape moves on the surface of the sphere. Left click to place the face on the sphere. You can place the first face anywhere, but all succeeding faces must be joined to existing faces at two points. (A picture of the basic sphere solid is provided at the bottom left of the tool box for face location reference.) In order to position the faces to be added, the right mouse button held down allows rotation of the face. By moving the mouse forward or backward with the right button down, the face will rotate. Release the button when the face is close to where you want it. Exact positioning is not required. As long as the connecting points are within 1/3 edge length, the program will know which points you wish to join. Left click to add the face. > ADD, AREA mode --> Used after the sphere has undergone a breakdown to smaller faces. Use this tool when you have deleted faces you wish to restore, or just fill an area with faces. The computer will attempt to figure out the best configuration for faces to add in the selected area. Draw your area around at least 3 points. (See 'Using FACE or AREA mode' for drawing the working area) > DEL This tool deletes selected faces from the sphere. (See 'Using FACE or AREA mode' for selecting faces) If you delete faces you want back, use the ADD tool in AREA mode. > BREAKDOWN This tool initiates a breakdown of the working sphere into smaller faces. You can select between several breakdowns. Additional breakdowns may be performed later to further reduce the face sizes. The frequency of the breakdown indicates how many sections each edge is divided into. (4 frequency divides each edge into 4 lengths) By observing the edge lengths status data displayed on the left of the screen, you can determine just how far you want to break the sphere down to meet material requirements for the construction of your dome. Adjustments to the radius (SPHERES drop-down menu) will increase or decrease the edge lengths. Triacon breakdowns change the edges. Two triacon breakdowns in a row restore the original edges, with a three frequency breakdown result. To use this tool, left-click on the BREAKDOWN tool and select your choice from the selections box which appears. > CUT SPHERE This tool will shear your sphere into a dome with a flat base. Further cuts can be performed later to further reduce the dome height. In order to cut a sphere, three points need to be selected around the sphere to define a flat plane for the base. To use this tool, first left-click on the CUT SPHERE tool. Then move the mouse into the working area to the left. You will be prompted to select the first point, and a line will appear on the sphere. Move the mouse close to your selected point... the line should move to that level and the point you want should have a circle around it. (Right click to abort) When you have the point where you want it, left-click the mouse. The sphere is then rotated 120 degrees (1/3 rotation) and you are prompted for the second point. (the first point will be visible for reference) Again, select the point desired as done above, and the sphere is again rotated 120 degrees for the third point. This time, the line becomes an ellipse defining a plane. As you move the mouse to different points, the new plane is calculated and the ellipse follows the cut line. Again, left-click on your point. Now the sphere is rotated for the flat base and redrawn. You are prompted "Cut Here?" and must answer with Y to perform the cut. A selection box appears for the determination of which way you wish to cut the sphere. --> CUT will shear the faces along the base, increasing the number of face points. --> MOVE will move points below the base up to the base, modifying the face shape. This yields different face shapes. Note: this is only performed if all base faces are triangles, else the CUT is performed. --> MOVE NEAR POINTS will move any close points to the base if possible which makes for fewer small faces and larger base faces. --> TRY FOR CIRCLE will attempt to move base points which have been cut to the circle formed where the base plane cuts the sphere. Trapezoids (4 point faces) will have their bottom lines extended the the circle. A word of caution: This may form tall narrow triangles in the base. If your sphere has not been saved prior to this function, a SAVE operation is performed first before the cut. Enter the name you want to save the sphere under. (You need not enter the .GEO... the program will do this for you.) > DISP This tool is a convenience for creating basic sphere solids. It toggles between Clear Front Faces and All Solid Out, Dotted In. Sometimes you cannot see where to add a new face when building your sphere. This switches the display mode to show rear faces. You could build your sphere with all faces showing, but it takes longer to draw the sphere. Clear Front Faces is relatively fast. > CIRCLE The displayed reference circle with cross-hairs can be toggled on or off with this tool. > ROTATION These tools are the arrows. They allow rotation of the sphere in 10 different directions. The amount of rotation is determined by the current selection under the ROTATE drop-down menu. Left-clicking in an arrow will perform a sphere rotation in the desired direction. Right-clicking on an arrow will continuously rotate the sphere until another mouse click is done. > HOME This tool resides in the center of the rotate tools, and will rotate the sphere to the home position (previously set with the 'Set Home' selection under the ROTATE drop-down menu). > CAMERA This tool will create a series of pictures of your sphere, each picture from a different rotated view. When finished, the MOVIE tool is used to display the pictures. When this tool is left-clicked on, you are prompted for the number of pictures you want for a full 360 degree display. The more the pictures, the smoother the MOVIE display, but the longer it will take to generate and potentially the smaller each picture will be depending on available memory. Also, you can select which mode to display your picture, and rotation direction. If you have 3D Stereo-Tek glasses, 72 pictures are required and the rotation must be left-right. Since the CAMERA function uses a tremendous amount of memory, further sphere work is not possible without first unloading the memory. This is accomplished by re-entering the Camera tool, allow the tool to clear memory, then abort the generation of a new new movie. > MOVIE This tool is available when the Camera tool has been used, or a movie has been loaded from disk. Activate it by left-clicking on the tool. It provides a fast rotating display of your sphere in two modes which are toggled with the left mouse button. Right-click to exit. Mode 1. Left-right motion of the mouse rotates the display in proportion to the position of the mouse. Mode 2. The sphere continually rotates in the direction the mouse is moved. The speed of rotation is controlled by the distance you move the mouse. Basic Solids The general idea of this program is to first create the basic spherical solids you wish to use and saving them to disk. Once created, they can be used repeatedly to generate complex spheres and domes. Basic spherical solids are made by selecting the type of solid from the SPHERES dropdown menu, then using the ADD tool (in FACE mode) to place the face shapes in place. This is the 'puzzle' aspect of the program. Complete solids can only be be made when the faces are placed in their correct positions. As an aid, only the correct face types are available to be selected, and a graphic picture of a complete sphere is shown for reference. Once the basic solid is complete, it should be rotated to the orientation of your preference, then saved to disk under a descriptive name. (example: An ICOSOHEDRON is generated, then saved as "ICOSAHED.GEO" to the disk.) You may also wish to set the radius of the sphere prior to saving it. > Modifying a Basic Solid To generate a geodesic structure, load (if not already in memory) the basic spherical solid you wish to work with. Then using the various tools in the TOOLS box and drop-down menu items, proceed to modify the basic spherical solid by break-downs, cut the base (if desired), toggle window faces to see through, and save the new geodesic to disk under a different name than the basic spherical solid (or else you will lose your basic solid and will need to regenerate it). > Using your Geodesic Several things can be done with your geodesic sphere. 1. Select the display mode desired, select the rotation increments, and use the rotate tools to view from different angles. 2. Select the CAMERA tool, and generate a 'movie' for fast rotation display. Then click on the MOVIE tool and move the mouse. 3. Save the geodesic to disk using the DEGAS function under the FILE drop-down menu. The created picture can then be loaded into the DEGAS or DEGAS-ELITE paint program for picture painting. 4. Print the geodesic to your graphical printer. --- You can print a picture only of your geodesic. --- You can print detailed construction information for creating a model or a shell for a house. (I have not actually constructed one yet. If one of you people actually uses this program for construction, please let me know the results. The program (in theory) should create useable information for construction. Construction information is in two forms: Faces only... suitable for paper constructions. No thickness information is used, so the actual face outside dimensions only are generated. Full Detailed Construction... uses wood thickness and sizes to modify output dimensions. Framing, outside and inside face dimensions (adjusted for thickness and angles) are generated. The method of framing uses right angle techniques for easy construction.