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Mueller, Copyright (c) 2005, 2006, 2007, last updated Tue, January 29, 2019 The Rhombicuboctahedron Rhombicuboctahedron Uniform Polyhedron: U10 aka Small Rhombicuboctahedron Archimedean Solid: A6 Vertices: 24 Edges: 48 Faces: 26 Wythoff symbol: 3 4|2 Symmetry Group: octahedral Vertex Configuration: {4, 3, 4, 4} Dual: deltoidal icositetrahedron V: s3 / 3 * (12 + 10 * √2) A: s2 * (18 + 2 * √3) rinner: s / 17 * (6 + √2) * √(5 + 2 * √2) router: s / 2 * √(5 + 2 * √2) s = , V = , A = , rinner = , router = , ravg = Preparing the Rhombicuboctahedron Rhombicuboctahedron L0/0V (original) Rhombicuboctahedron L1/1V flat (only triangles & flat) Rhombicuboctahedron L1/1V (only triangles & normalized) The squares are triangulated for further processing. 1V/L1 3/8 Rhombicuboctahedron Dome Geodesic 1V 3/8 Rhombicuboctahedron Dome (front view) Geodesic 1V 3/8 Rhombicuboctahedron Dome (bird view) vertices/connectors: 17 13 x 4-way 4 x 7-way 1V 3/8 Rhombicuboctahedron Dome Construction Map edges/struts & bending angles (αstrut): A x 20: 0.52372 (15.18°) B x 20: 0.71481 (20.94°) total 40 struts (2 kinds)1) strut variance 36.5% faces: 24 (3-sided) A-A-B x 20 (46.96°, 46.96°, 86.07°) B-B-B x 4 (60.00°, 60.00°, 60.00°) 2 kinds of faces2) diameter: 2.000, radius: 1.000 height: 0.643 or 32.14% 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 1V 3/8 Rhombicuboctahedron Dome Calculator Geodesic 1V 3/8 Rhombicuboctahedron Dome (Human is 170cm/5'7") d = , lhole = (Edit numbers & hit TAB to recalculate) Alath = x 20, Blath = x 20, h = 1V/L1 5/8 Rhombicuboctahedron Dome Geodesic 1V 5/8 Rhombicuboctahedron Dome (front view) Geodesic 1V 5/8 Rhombicuboctahedron Dome (bird view) vertices/connectors: 33 13 x 4-way 8 x 5-way 12 x 7-way 1V 5/8 Rhombicuboctahedron Dome Construction Map edges/struts & bending angles (αstrut): A x 52: 0.52372 (15.18°) B x 36: 0.71481 (20.94°) total 88 struts (2 kinds)1) strut variance 36.5% faces: 56 (3-sided) A-A-B x 52 (46.96°, 46.96°, 86.07°) B-B-B x 4 (60.00°, 60.00°, 60.00°) 2 kinds of faces2) diameter: 2.000, radius: 1.000 height: 1.358 or 67.88% 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 1V 5/8 Rhombicuboctahedron Dome Calculator Geodesic 1V 5/8 Rhombicuboctahedron Dome (Human is 170cm/5'7") d = , lhole = (Edit numbers & hit TAB to recalculate) Alath = x 52, Blath = x 36, h = This is a nice variant, with square walls, optionally instead of square triangulation either replaced by one strut (B * √2) or leave it out at all. The vertical struts of the vertical wall make it look very artistic, yet also edgy, but given it's a 1V it's understandable. With only 88 struts you get a 5/8 sphere. At d = 6m the height is apprx. 4m and a 2nd level can be done at 2m height, just at the level of existing connectors. 2V/L2 3/8 Rhombicuboctahedron Dome Geodesic 2V 3/8 Rhombicuboctahedron Dome (front view) Geodesic 2V 3/8 Rhombicuboctahedron Dome (bird view) vertices/connectors: 57 21 x 4-way 32 x 6-way 4 x 7-way 2V 3/8 Rhombicuboctahedron Dome Construction Map edges/struts & bending angles (αstrut): A x 40: 0.26418 (7.59°) B x 40: 0.27386 (7.87°) C x 40: 0.36346 (10.47°) D x 20: 0.37033 (10.67°) E x 12: 0.38268 (11.03°) total 152 struts (5 kinds)1) strut variance 44.9% faces: 96 (3-sided) A-A-D x 20 (45.51°, 45.51°, 88.98°) A-B-C x 40 (46.39°, 48.64°, 84.97°) B-B-D x 20 (47.47°, 47.47°, 85.06°) C-C-E x 12 (58.24°, 58.24°, 63.53°) E-E-E x 4 (60.00°, 60.00°, 60.00°) 5 kinds of faces2) diameter: 2.000, radius: 1.000 height: 0.643 or 32.14% 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 3/8 Rhombicuboctahedron Dome Calculator Geodesic 2V 3/8 Rhombicuboctahedron Dome (Human is 170cm/5'7") d = , lhole = (Edit numbers & hit TAB to recalculate) Alath = x 40, Blath = x 40, Clath = x 40, Dlath = x 20, Elath = x 12, h = 2V/L2 5/8 Rhombicuboctahedron Dome Geodesic 2V 5/8 Rhombicuboctahedron Dome (front view) Geodesic 2V 5/8 Rhombicuboctahedron Dome (bird view) vertices/connectors: 121 21 x 4-way 8 x 5-way 80 x 6-way 12 x 7-way 2V 5/8 Rhombicuboctahedron Dome Construction Map edges/struts & bending angles (αstrut): A x 104: 0.26418 (7.59°) B x 104: 0.27386 (7.87°) C x 72: 0.36346 (10.47°) D x 52: 0.37033 (10.67°) E x 12: 0.38268 (11.03°) total 344 struts (5 kinds)1) strut variance 44.9% faces: 224 (3-sided) A-A-D x 52 (45.51°, 45.51°, 88.98°) A-B-C x 104 (46.39°, 48.64°, 84.97°) B-B-D x 52 (47.47°, 47.47°, 85.06°) C-C-E x 12 (58.24°, 58.24°, 63.53°) E-E-E x 4 (60.00°, 60.00°, 60.00°) 5 kinds of faces2) diameter: 2.000, radius: 1.000 height: 1.383 or 69.14% 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 5/8 Rhombicuboctahedron Dome Calculator Geodesic 2V 5/8 Rhombicuboctahedron Dome (Human is 170cm/5'7") d = , lhole = (Edit numbers & hit TAB to recalculate) Alath = x 104, Blath = x 104, Clath = x 72, Dlath = x 52, Elath = x 12, h = This is also a nice variant, alike the 1V 5/8 one. Multiple squares in a spherical setting, a nice crossover of rectangular to circular/spherical space. With 344 struts still considerable for temporary buildings. 3V 3/8 Rhombicuboctahedron Dome Geodesic 3V 3/8 Rhombicuboctahedron Dome (front view) Geodesic 3V 3/8 Rhombicuboctahedron Dome (bird view) vertices/connectors: 121 29 x 4-way 88 x 6-way 4 x 7-way 3V 3/8 Rhombicuboctahedron Dome Construction Map edges/struts & bending angles (αstrut): A x 40: 0.17453 (5.01°) B x 20: 0.18015 (5.17°) C x 40: 0.18031 (5.17°) D x 40: 0.18048 (5.18°) E x 40: 0.18562 (5.33°) F x 40: 0.23805 (6.84°) G x 20: 0.24588 (7.06°) H x 40: 0.24779 (7.12°) I x 32: 0.25307 (7.27°) J x 24: 0.25516 (7.33°) total 336 struts (10 kinds)1) strut variance 46.2% faces: 216 (3-sided) A-A-G x 20 (45.20°, 45.20°, 89.59°) A-D-F x 40 (46.82°, 48.96°, 84.22°) B-C-H x 40 (46.56°, 46.59°, 86.85°) C-C-G x 20 (47.01°, 47.01°, 85.99°) D-E-H x 40 (46.54°, 48.28°, 85.19°) E-E-I x 20 (47.01°, 47.01°, 85.98°) F-F-I x 12 (57.89°, 57.89°, 64.21°) I-J-J x 24 (59.46°, 60.27°, 60.27°) 8 kinds of faces2) diameter: 2.000, radius: 1.000 height: 0.643 or 32.14% 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 3/8 Rhombicuboctahedron Dome Calculator Geodesic 3V 3/8 Rhombicuboctahedron Dome (Human is 170cm/5'7") d = , lhole = (Edit numbers & hit TAB to recalculate) Alath = x 40, Blath = x 20, Clath = x 40, Dlath = x 40, Elath = x 40, Flath = x 40, Glath = x 20, Hlath = x 40, Ilath = x 32, Jlath = x 24, h = 3V 5/8 Rhombicuboctahedron Dome Geodesic 3V 5/8 Rhombicuboctahedron Dome (front view) Geodesic 3V 5/8 Rhombicuboctahedron Dome (bird view) vertices/connectors: 265 29 x 4-way 8 x 5-way 216 x 6-way 12 x 7-way 3V 5/8 Rhombicuboctahedron Dome Construction Map edges/struts & bending angles (αstrut): A x 104: 0.17453 (5.01°) B x 52: 0.18015 (5.17°) C x 104: 0.18031 (5.17°) D x 104: 0.18048 (5.18°) E x 104: 0.18562 (5.33°) F x 72: 0.23805 (6.84°) G x 52: 0.24588 (7.06°) H x 104: 0.24779 (7.12°) I x 48: 0.25307 (7.27°) J x 24: 0.25516 (7.33°) total 768 struts (10 kinds)1) strut variance 46.2% faces: 504 (3-sided) A-A-G x 52 (45.20°, 45.20°, 89.59°) A-D-F x 104 (46.82°, 48.96°, 84.22°) B-C-H x 104 (46.56°, 46.59°, 86.85°) C-C-G x 52 (47.01°, 47.01°, 85.99°) D-E-H x 104 (46.54°, 48.28°, 85.19°) E-E-I x 52 (47.01°, 47.01°, 85.98°) F-F-I x 12 (57.89°, 57.89°, 64.21°) I-J-J x 24 (59.46°, 60.27°, 60.27°) 8 kinds of faces2) diameter: 2.000, radius: 1.000 height: 1.380 or 68.99% 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 5/8 Rhombicuboctahedron Dome Calculator Geodesic 3V 5/8 Rhombicuboctahedron Dome (Human is 170cm/5'7") d = , lhole = (Edit numbers & hit TAB to recalculate) Alath = x 104, Blath = x 52, Clath = x 104, Dlath = x 104, Elath = x 104, Flath = x 72, Glath = x 52, Hlath = x 104, Ilath = x 48, Jlath = x 24, h = 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 ... 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