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Müller Geodesic Solitude Johnny's Capsule Geodesic Clay Mud Dome Jurtendorf (Switzerland) Neolithics of Pfyn Strawbale Cabin Dome Geodesic Dome Geodesic Dome Notes & Calculator Table of Content Introduction Overview of Variants How to Use the Notes Strut Options & Notion The Icosahedron The Octahedron The Cube The Cuboctahedron The Truncated Octahedron The Rhombicuboctahedron Building Models Real Life Application Links Geodesic Dome Diary Geodesic Polyhedra Polyhedra Notes Bow Dome Triangulated Bow Dome Star Dome Star Dome Diary Wigwam Zome Helix Zome Low Cost Dome (PVC) Miscellaneous Domes Site Search Enter term & press ENTER If you found the information useful, consider to make a donation:   Page << Prev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | Next >> Geodesic Dome Notes & Calculator written by Rene K. Mueller, Copyright (c) 2005, 2006, 2007, last updated Tue, January 29, 2019 The Icosahedron Icosahedron Uniform Polyhedron: U22 Platonic Solid Platonic Element: Water Vertices: 12 Edges: 30 Faces: 20 Wythoff symbol: 5|2 3 Symmetry Group: icosahedral Vertex Configuration: {3, 3, 3, 3, 3} Dual: dodecahedron V: s3 * 5/12 * (3 + √5) A: s2 * 20 / 4 * √3 rinner: s / 12 * (3 * √3 + √15) router: s / 4 * √(10 + 2 * √5) s = , V = , A = , rinner = , router = , ravg = 1V/L1 2/3 Icosahedron Dome Geodesic 1V 2/3 Icosahedron Dome (front view) Geodesic 1V 2/3 Icosahedron Dome (bird view) vertices/connectors: 11 5 x 4-way 6 x 5-way 1V 2/3 Icosahedron Dome Construction Map edges/struts & bending angles (αstrut): A x 25: 1.05146 (31.72°) faces: 15 (3-sided) A-A-A x 15 (60.00°, 60.00°, 60.00°) diameter: 2.000, radius: 1.000 height: 1.447 or 72.36% of diameter 1V 2/3 Icosahedron Dome Calculator Geodesic 1V 2/3 Icosahedron Dome (Human is 170cm/5'7") d = , lhole = (Edit numbers & hit TAB to recalculate) Alath = x 25, h = 2V/L2 Icosahedron Dome Geodesic 2V Icosahedron Dome (front view) Geodesic 2V Icosahedron Dome (bird view) vertices/connectors: 26 10 x 4-way 6 x 5-way 10 x 6-way 2V Icosahedron Dome Construction Map edges/struts & bending angles (αstrut): A x 30: 0.54653 (15.86°) B x 35: 0.61803 (18.00°) total 65 struts (2 kinds)1) strut variance 13.1% faces: 40 (3-sided) A-A-B x 30 (55.57°, 55.57°, 68.86°) B-B-B x 10 (60.00°, 60.00°, 60.00°) 2 kinds of faces2) diameter: 2.000, radius: 1.000 height: 1.000 or 50.00% of diameter 1) strut lengths sorted by 1/10'000th or +/-0.00005 exact 2) clock wise (cw) and counter clock wise (ccw) orientation neglected 2V Icosahedron Dome Calculator Geodesic 2V Icosahedron Dome (Human is 170cm/5'7") d = , lhole = (Edit numbers & hit TAB to recalculate) Alath = x 30, Blath = x 35, h = Cut optimization: normalize Alath+Blath = 1.0, therefore Alath+Blath = cuts: 30 x (Alath+Blath): 5 x (Blath): total 35 laths to cut 3V 4/9 Icosahedron Dome In some literature this variant is also called "3V 3/8 Dome". Geodesic 3V 4/9 Icosahedron Dome (front view) Geodesic 3V 4/9 Icosahedron Dome (bird view) vertices/connectors: 46 15 x 4-way 6 x 5-way 25 x 6-way 3V 4/9 Icosahedron Dome Construction Map edges/struts & bending angles (αstrut): A x 30: 0.34862 (10.04°) B x 40: 0.40355 (11.64°) C x 50: 0.41241 (11.90°) total 120 struts (3 kinds)1) strut variance 18.3% faces: 75 (3-sided) A-A-B x 30 (54.63°, 54.63°, 70.74°) B-C-C x 45 (58.59°, 60.70°, 60.70°) 2 kinds of faces2) diameter: 2.000, radius: 1.000 height: 0.828 or 41.42% of diameter 1) strut lengths sorted by 1/10'000th or +/-0.00005 exact 2) clock wise (cw) and counter clock wise (ccw) orientation neglected 3V 4/9 Icosahedron Dome Calculator Geodesic 3V 4/9 Icosahedron Dome (Human is 170cm/5'7") d = , lhole = (Edit numbers & hit TAB to recalculate) Alath = x 30, Blath = x 40, Clath = x 50, h = Cut optimization: normalize Blath+Clath = 1.0, therefore Blath+Clath = cuts: 40 x (Blath+Clath): 10 x (Alath+Clath): 10 x (Alath+Alath): total 60 laths to cut As you see the bottom isn't entirely even, for heavy construction you have to level them. 3V 5/9 Icosahedron Dome In some literature this variant is also called "3V 5/8 Dome". Geodesic 3V 5/9 Icosahedron Dome (front view) Geodesic 3V 5/9 Icosahedron Dome (bird view) vertices/connectors: 61 15 x 4-way 6 x 5-way 40 x 6-way 3V 5/9 Icosahedron Dome Construction Map edges/struts & bending angles (αstrut): A x 30: 0.34862 (10.04°) B x 55: 0.40355 (11.64°) C x 80: 0.41241 (11.90°) total 165 struts (3 kinds)1) strut variance 18.3% faces: 105 (3-sided) A-A-B x 30 (54.63°, 54.63°, 70.74°) B-C-C x 75 (58.59°, 60.70°, 60.70°) 2 kinds of faces2) diameter: 2.000, radius: 1.000 height: 1.188 or 59.38% of diameter 1) strut lengths sorted by 1/10'000th or +/-0.00005 exact 2) clock wise (cw) and counter clock wise (ccw) orientation neglected 3V 5/9 Icosahedron Dome Calculator Geodesic 3V 5/9 Icosahedron Dome (Human is 170cm/5'7") d = , lhole = (Edit numbers & hit TAB to recalculate) Alath = x 30, Blath = x 55, Clath = x 80, h = Cut optimization: normalize Blath+Clath = 1.0, therefore Blath+Clath = cuts: 55 x (Blath+Clath): 25 x (Alath+Clath): 3 x (Alath+Alath): total 83 laths to cut As you see here as well that the bottom isn't entirely even, for heavy construction you have to level them. 4V Icosahedron Dome Geodesic 4V Icosahedron Dome (front view) Geodesic 4V Icosahedron Dome (bird view) vertices/connectors: 91 20 x 4-way 6 x 5-way 65 x 6-way 4V Icosahedron Dome Construction Map edges/struts & bending angles (αstrut): A x 30: 0.25318 (7.27°) B x 60: 0.29453 (8.47°) C x 30: 0.29524 (8.49°) D x 30: 0.29859 (8.59°) E x 70: 0.31287 (9.00°) F x 30: 0.32492 (9.35°) total 250 struts (6 kinds)1) strut variance 28.3% faces: 160 (3-sided) A-A-C x 30 (54.34°, 54.34°, 71.32°) B-B-C x 30 (59.92°, 59.92°, 60.16°) B-D-E x 60 (57.52°, 58.80°, 63.68°) E-E-F x 30 (58.72°, 58.72°, 62.55°) F-F-F x 10 (60.00°, 60.00°, 60.00°) 5 kinds of faces2) diameter: 2.000, radius: 1.000 height: 1.000 or 50.00% of diameter 1) strut lengths sorted by 1/10'000th or +/-0.00005 exact 2) clock wise (cw) and counter clock wise (ccw) orientation neglected 4V Icosahedron Dome Calculator Geodesic 4V Icosahedron Dome (Human is 170cm/5'7") d = , lhole = (Edit numbers & hit TAB to recalculate) Alath = x 30, Blath = x 60, Clath = x 30, Dlath = x 30, Elath = x 70, Flath = x 30, h = Cut optimization: normalize Elath+Elath = 1.0, therefore Elath+Elath = cuts: 60 x (Blath+Elath): 5 x (Elath+Elath): 30 x (Alath+Flath): 30 x (Clath+Dlath): total 125 laths to cut The 4V looks very attractive, yet, I would recommend using the L3 version instead with less strut lengths and less strut variance. L3 Icosahedron Dome Geodesic L3 Icosahedron Dome (front view) Geodesic L3 Icosahedron Dome (bird view) vertices/connectors: 91 20 x 4-way 6 x 5-way 65 x 6-way L3 Icosahedron Dome Construction Map edges/struts & bending angles (αstrut): A x 60: 0.27590 (7.93°) B x 60: 0.28547 (8.21°) C x 70: 0.31287 (9.00°) D x 30: 0.32124 (9.24°) E x 30: 0.32492 (9.35°) total 250 struts (5 kinds)1) strut variance 17.8% faces: 160 (3-sided) A-A-D x 30 (54.40°, 54.40°, 71.20°) A-B-C x 60 (54.68°, 57.60°, 67.72°) B-B-D x 30 (55.77°, 55.77°, 68.46°) C-C-E x 30 (58.72°, 58.72°, 62.55°) E-E-E x 10 (60.00°, 60.00°, 60.00°) 5 kinds of faces2) diameter: 2.000, radius: 1.000 height: 1.000 or 50.00% of diameter 1) strut lengths sorted by 1/10'000th or +/-0.00005 exact 2) clock wise (cw) and counter clock wise (ccw) orientation neglected L3 Icosahedron Dome Calculator Geodesic L3 Icosahedron Dome (Human is 170cm/5'7") d = , lhole = (Edit numbers & hit TAB to recalculate) Alath = x 60, Blath = x 60, Clath = x 70, Dlath = x 30, Elath = x 30, h = Cut optimization: normalize Clath+Clath = 1.0, therefore Clath+Clath = cuts: 60 x (Blath+Clath): 5 x (Clath+Clath): 30 x (Alath+Dlath): 30 x (Alath+Elath): total 125 laths to cut The L3 might be a better choice for a 250 strut dome than the 4V variant: the L3 provides less strut variance 17.8% (5 kinds of struts) instead of 28.3% (6 kinds of struts). Next Page >> Page << Prev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | Next >> Content: Page 1: Table of Content, Changes Page 2: Introduction, Origin of the Geodesic Dome, Geodesize: Triangulate & Normalize, Procedure & Evolution of a Subdividing Triangle ... Page 3: Overview of Variants, Numerical Overview, Amount of Struts vs. Strut Variance, Amount of Struts vs. Strut Types ... Page 4: The Icosahedron, 1V/L1 2/3 Icosahedron Dome, 2V/L2 Icosahedron Dome, 3V 4/9 Icosahedron Dome ... Page 5: 5V 7/15 Icosahedron Dome, 5V 8/15 Icosahedron Dome, 6V Icosahedron Dome, 2V.3V Icosahedron Dome ... Page 6: 7V 10/21 Icosahedron Dome, 7V 11/21 Icosahedron Dome, 8V Icosahedron Dome, L4 Icosahedron Dome ... Page 7: The Octahedron, 1V/L1 Octahedron Dome, 2V/L2 Octahedron Dome, 3V Octahedron Dome Page 8: 4V Octahedron Dome, L3 Octahedron Dome, L3 1/4 Octahedron Dome, L3 5/8 Octahedron Dome Page 9: 5V Octahedron Dome, 6V Octahedron Dome, 2V.3V Octahedron Dome, 3V.2V Octahedron Dome Page 10: 7V Octahedron Dome, 8V Octahedron Dome, L4 Octahedron Dome, L4 7/16 Octahedron Dome, L4 9/16 Octahedron Dome ... Page 11: 9V Octahedron Dome, 3V.3V Octahedron Dome, 10V Octahedron Dome, 2V.5V Octahedron Dome, 2V.5V Octahedron Dome ... Page 12: The Cube, Preparing the Cube, 1V/L1 Cube Dome, 2V/L2 Cube Dome, 3V Cube Dome, 4V Cube Dome, L3 Cube Dome ... Page 13: 5V Cube Dome, 6V Cube Dome, 2V.3V Cube Dome, 3V.2V Cube Dome, 7V Cube Dome Page 14: The Cuboctahedron, Preparing the Cuboctahedron, 1V/L1 Cuboctahedron Dome, 2V/L2 Cuboctahedron Dome ... Page 15: 5V Cuboctahedron Dome, 6V Cuboctahedron Dome, 2V.3V Cuboctahedron Dome, 3V.2V Cuboctahedron Dome ... Page 16: The Truncated Octahedron, Preparing the Truncated Octahedron, 1V/L1 Truncated Octahedron Dome ... Page 17: The Rhombicuboctahedron, Preparing the Rhombicuboctahedron, 1V/L1 3/8 Rhombicuboctahedron Dome ... Page 18: Building Models, 3V 5/9 Icosahedron Model, 2V Icosahedron Model, 4V Icosahedron Model, 2V/L2 Cuboctahedron Model ... Page 19: Real Life Application, Options, Connectors, Separate Functions, Cover, 4/8 Sphere Cover Calculator ... Home   ·   About   ·   Tipi   ·   Yurt   ·   Dome   ·   Features   ·   Gallery Print   ·   Bookmark Creative Commons (CC) BY-SA-NC 2005-2017, developed, designed and written by René K. Müller Graphics & illustrations made with Inkscape, Tgif, Gimp, PovRay, GD.pm Web-Site powered by FreeBSD & Debian/Linux - 100% Open Source