![]() geodesic dome over south pole |
![]() geodesic dome at Expo '67, Montreal |
![]() geodesic dome "Spaceship Earth" at EPCOT, Walt Disney Wolrd, Florida |
![]() geodesic dome playground equipment |
"An icosahedron and related symmetry polyhedra can be used to define a high geodesic polyhedron by dividing triangular faces into smaller triangles, and projecting all the new vertices onto a sphere. Higher order polygonal faces can be divided into triangles by adding new vertices centered on each face. The new faces on the sphere are not equilateral triangles, but they are approximately equal edge length."
— Wikipedia article on Geodesic polyhedron
Start with a polyhedron. |
Triangulate all polygons having more than 3 sides by adding a central point (if needed). |
Pick a frequency f > 1. Divide each edge into f segments by adding points; add interior points as needed. Turn each original triangle into a mesh of f2 triangles. |
"Puff" the shape out to a set of points on a unit sphere, by moving each point towards or away from the origin until its distance from the origin is one. |
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Click an image to open an interactive 3D app.
seed name | seed (1-freq) | 2-freq | 3-freq | 4-freq | 5-freq | 10-freq | ||||||||||
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tetrahedron four faces (triangles) one of the five Platonic Solids dual of itself space filling with the octahedron nicknames: triangle-base pyramid, D-4
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tetAGeod4.html |
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seed name | seed (1-freq) | 2-freq | 3-freq | 4-freq | 5-freq | 10-freq | ||||||||||
cube six faces (squares) one of the five Platonic Solids dual of the octahedron space filling nicknames: hexahedron, D-6
Note: each square is split |
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cubeAGeod4.html | |||||||||||||
seed name | seed (1-freq) | 2-freq | 3-freq | 4-freq | 5-freq | 10-freq | ||||||||||
octahedron eight faces (triangles) one of the five Platonic Solids dual of the cube space filling with the tetrahedron nicknames: pyramid on a mirror, D-8
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seed name | seed (1-freq) | 2-freq | 3-freq | 4-freq | 5-freq | 10-freq | ||||||||||
dodecahedron twelve faces (pentagons) one of the five Platonic Solids dual of the icosahedron nicknames: D-12
Note: each pentagon is split |
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dodecAGeod4.html | ||||||||||||||
seed name | seed (1-freq) | 2-freq | 3-freq | 4-freq | 5-freq | 10-freq | ||||||||||
icosahedron twenty faces (triangles) one of the five Platonic Solids dual of the dodecahedron nicknames: D-20
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![]() icosVGeod2.html no facets, lines, spheres, no puff
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icosAGeod5.html |
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seed name | seed (1-freq) | 2-freq | 3-freq | 4-freq | 5-freq | 10-freq | ||||||||||
snub cube 38 faces (32 triangles, 6 squares) one of the thirteen Archimedean Solids dual of the pentagonal icositetrahedron nicknames: snic
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snubcAGeod4.html | |||||||||||||
seed name | seed (1-freq) | 2-freq | 3-freq | 4-freq | 5-freq | 10-freq | ||||||||||
rhombic dodecahedron twelve faces (rhombuses one of the thirteen Catalan Solids dual of the cuboctahedron space filling
Note: each rhombus is split |
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rhombicAGeod3.html | ![]() rhombicVGeod10.html no facets, lines, spheres, no puff
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seed name | seed (1-freq) | 2-freq | 3-freq | 4-freq | 5-freq | 10-freq | ||||||||||
cuboctahedron 14 faces (8 triangles, 6 squares) dual of the rhombic dodecahedron
nicknames: jitterbug, Vector
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cuboctAGeod2.html![]() cuboctVGeod2.html no facets, lines, spheres, no puff
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![]() cuboctVGeod10.html no facets, lines, spheres, no puff
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seed name | seed (1-freq) | 2-freq | 3-freq | 4-freq | 5-freq | 10-freq |
filename taxonomy: [mode][seed][options]Geod[f] mode: Run production mode Test debug writes, comnpare to good output seed: Cube [6 tri] Cuboct Dodec [12 pen] Icos [20 tri] Oct [8 tri] Rhombic [12 rho] Tet [4 tri] options: N - no spheres (default = yes spheres) V - vectors only (all have vectors) W - white faces C - color faces F - flat facets P - "puffed" facets