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Müller Geodesic Solitude Johnny's Capsule Geodesic Clay Mud Dome Jurtendorf (Switzerland) Neolithics of Pfyn Dome Geodesic Dome Geodesic Dome Notes Geodesic Dome Diary Geodesic Polyhedra Polyhedra Notes Introduction Platonic Solids Archimedean Solids Johnson Solids Uniform Polyhedra Waterman Polyhedra Bow Dome Triangulated Bow Dome Star Dome Star Dome Diary Wigwam Zome Helix Zome 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 | Next >> Polyhedra Notes written by Rene K. Mueller, Copyright (c) 2007, last updated Wed, January 9, 2008 Square Pyramid Square Pyramid Johnson Solid: J1 Vertices: 5 Faces: 5 Edges: 8 V: s3 / 6 * √2 A: s2 * (1 + √3) General Pyramid The general pyramid: q = √((s/2)2 + h2) l = √((s/2)2 + q2) A = 2 s q + s2 Awall/roof = 2 s q V = s2 h / 3 Historic Pyramids The Pyramids of Giza (courtesy Bruno Girin/DHD Multimedia Gallery ) Most obvious association with pyramids comes from the egyptian pyramids in Giza and those of the mayans in south america. It is also apparent those pyramids have been built with enormous effort and skills which is now honored by the durability of thousands of years. The largest pyramid in Giza is the Khufu Pyramid, with following values: s = 231m (original) (now: 230.4m) h = 146.6m (original) (now: 138.8m) thereby q = 186.632m l = 219.478m Interesting ratio: s/h = 1.57571.. ~ π/2 ~ 11/7 Read more at Great Pyramid of Giza . Pentagonal Pyramid Pentagonal Pyramid Johnson Solid: J2 Vertices: 6 Faces: 6 Edges: 10 V: s3 / 24 * (5 + √5) A: s2 / 2 * √(5/2 * (10 + √10 + √(75+30*√5)) The roof isn't very steep, unless those roof struts would be made longer - it would be a very simplistic habitat. Triangular Cupola Triangular Cupola Johnson Solid: J3 Vertices: 9 Faces: 8 Edges: 15 V: s3 * (5/(5*√2)) A: s2 * (3+5/2*√3) Square Cupola Square Cupola Johnson Solid: J4 Vertices: 12 Faces: 10 Edges: 20 Also cap of a Rhombicuboctahedron. Pentagonal Cupola Pentagonal Cupola Johnson Solid: J5 Vertices: 15 Faces: 12 Edges: 25 V: s3 / 6 * (5+4*√5) A: s2 / 4 * (20+√(10*(80+31*√5+√(2175+950*√5)))) Also cap of a Rhombicosidodecahedron. Pentagonal Rotunda Pentagonal Rotunda Johnson Solid: J6 Vertices: 20 Faces: 17 Edges: 35 V: s3 / 12 * (45+17*√5) A: s2 * 5/2 * (√3+√(26+(58/√5))) h: s * √(1/5*(5+2*√5)) Also 1/2 of a Icosidodecahedron. Elongated Triangular Pyramid Elongated Triangular Pyramid Johnson Solid: J7 Vertices: 7 Faces: 7 Edges: 12 Elongated Square Pyramid Elongated Square Pyramid Johnson Solid: J8 Vertices: 9 Faces: 9 Edges: 16 Elongated Pentagonal Pyramid Elongated Pentagonal Pyramid Johnson Solid: J9 Vertices: 11 Faces: 11 Edges: 20 Gyroelongated Square Pyramid Gyroelongated Square Pyramid Johnson Solid: J10 Vertices: 9 Faces: 13 Edges: 20 Gyroelongated Pentagonal Pyramid Gyroelongated Pentagonal Pyramid Johnson Solid: J11 Vertices: 11 Faces: 16 Edges: 25 Triangular Dipyramid Triangular Dipyramid Johnson Solid: J12 Vertices: 5 Faces: 6 Edges: 9 Pentagonal Dipyramid Pentagonal Dipyramid Johnson Solid: J13 Vertices: 7 Faces: 10 Edges: 15 V: s3 / 12 * (5 + √5) A: s2 * 5/12 * √3 router: s / 10 * √(50+10*√5) h: s / 10 * √(50-10*√5) Elongated Triangular Dipyramid Elongated Triangular Dipyramid Johnson Solid: J14 Vertices: 8 Faces: 9 Edges: 15 Elongated Square Dipyramid Elongated Square Dipyramid Johnson Solid: J15 Vertices: 10 Faces: 12 Edges: 20 Elongated Pentagonal Dipyramid Elongated Pentagonal Dipyramid Johnson Solid: J16 Vertices: 12 Faces: 15 Edges: 25 Gyroelongated Square Dipyramid Gyroelongated Square Dipyramid Johnson Solid: J17 Vertices: 10 Faces: 16 Edges: 24 V: s3 * 2(1/4) / 4 * (1 + √2 + 2(1/4) ) A: s2 * 4 * √3 Elongated Triangular Cupola Elongated Triangular Cupola Johnson Solid: J18 Vertices: 15 Faces: 14 Edges: 27 Elongated Square Cupola Elongated Square Cupola Johnson Solid: J19 Vertices: 20 Faces: 18 Edges: 36 Elongated Pentagonal Cupola Elongated Pentagonal Cupola Johnson Solid: J20 Vertices: 25 Faces: 22 Edges: 45 Elongated Pentagonal Rotunda Elongated Pentagonal Rotunda Johnson Solid: J21 Vertices: 30 Faces: 27 Edges: 55 Very suitable for a habitat, the top smaller pentagon as skylight, and eventually the side pentagons further triangulated each. Gyroelongated Triangular Cupola Gyroelongated Triangular Cupola Johnson Solid: J22 Vertices: 15 Faces: 20 Edges: 33 Gyroelongated Square Cupola Gyroelongated Square Cupola Johnson Solid: J23 Vertices: 20 Faces: 26 Edges: 44 Gyroelongated Pentagonal Cupola Gyroelongated Pentagonal Cupola Johnson Solid: J24 Vertices: 25 Faces: 32 Edges: 55 Next Page >> Page << Prev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Next >> Content: Page 1: Introduction, Platonic Solids, Archimedean Solids, Tetrahedron, Truncated Tetrahedron, Octahedron ... Page 2: Johnson Solids Page 3: Square Pyramid, Historic Pyramids, Pentagonal Pyramid, Triangular Cupola, Square Cupola, Pentagonal Cupola ... Page 4: Gyroelongated Pentagonal Rotunda, Gyrobifastigium, Triangular Orthobicupola, Square Orthobicupola ... Page 5: Augmented Triangular Prism, Biaugmented Triangular Prism, Triaugmented Triangular Prism ... Page 6: Parabigyrate Rhombicosidodecahedron, Metabigyrate Rhombicosidodecahedron, Trigyrate Rhombicosidodecahedron ... Page 7: Uniform Polyhedra, References Page 8: Waterman Polyhedra, Some More Examples, Different Origins, Features of Waterman Polyhedra ... Home   ·   About   ·   Tipi   ·   Yurt   ·   Dome   ·   Features   ·   Gallery   ·   Links Print   ·   Contact   ·   Bookmark Creative Commons (CC) BY, NC 2005-2013, 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