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Topic: Triaugmented truncated dodecahedron


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In the News (Thu 28 Aug 14)

  
 [No title]
truncated dodecahedron +------------------------------------------------------------ The truncated dodecahedron is a polyhedron with 60 vertices and 42 faces.
triaugmented dodecahedron +------------------------------------------------------------ The triaugmented dodecahedron is a polyhedron with 23 vertices and 24 faces.
triaugmented truncated dodecahedron +------------------------------------------------------------ The triaugmented truncated dodecahedron is a polyhedron with 75 vertices and 62 faces.
www.math.harvard.edu /~knill/sofia/data/polyhedra.txt   (2272 words)

  
 Polyhedron - Wikipedia, the free encyclopedia
Classical polyhedra include the five regular convex polyhedra: tetrahedron (4 sides), cube (6 sides), octahedron (8 sides), dodecahedron (12 side) and icosahedron (20 sides), four regular non convex polyhedra (the Kepler-Poinsot solids), thirteen convex Archimedean solids and the 53 remaining uniform polyhedra.
Thus the regular polyhedra come in natural pairs: the dodecahedron with the icosahedron, the cube with the octahedron, and the tetrahedron with itself.
The rest are assembled by (pasting) combinations of the regular polyhedra described earlier: the dodecahedron, the small stellated dodecahedron, the great stellated dodecahedron and the great icosahedron.
en.wikipedia.org /wiki/Polyhedral   (1864 words)

  
 Icosahedron jerak.org   (Site not responding. Last check: 2007-08-31)
Finally, non-convex polytopes do not carry the same strict requirements as convex polytopes, and icosahedra are indeed the cells of the icosahedral 120-cell, one of the ten non-convex regular polychora.
Alternatively, using the nomenclature for snub polyhedra that refers to a snub cube as a snub cuboctahedron (cuboctahedron = Rectification (geometry) cube) and a snub dodecahedron as a snub icosidodecahedron (icosidodecahedron = rectified dodecahedron), one may call the icosahedron the snub octahedron (octahedron = rectified tetrahedron).
Despite appearances, when an icosahedron is inscribed in a sphere, it occupies less of the sphere's volume (60.54%) than a dodecahedron inscribed in the same sphere (66.49%).
icosahedron.en.jerak.org   (910 words)

  
 Polyhedron, Polyhedra, Polytopes - Numericana
The other three are the truncated octahedron (at left), the great rhombicosidodecahedron (at right) and the great rhombicuboctahedron.
Truncated: By cutting off an m-gonal pyramid at one or more (usually all) of the vertices.
Beyond F=4 (the tetrahedron of genus 0) and F=7 (the Szilassi heptahedron of genus 1) the next possibility would thus be F=12, a dodecahedron of genus 6...
home.att.net /~numericana/answer/polyhedra.htm   (5404 words)

  
 Cubic Circular, Issue 7 & 8
The rhombic dodecahedron is the dual of the cube-octahedron.
The rhombuses correspond to the edges of a cube or octahedron, The rhombic dodecahedron is the shape obtained by trimming a cube to octagonal cross sections along all three axes, then peaking all the face centres to square pyramids.
= E. The icosidodecahedron is similarly the truncation of the dodecahedron or the icosahedron.
geocities.com /jaapsch/puzzles/cubic7.htm   (13445 words)

  
 Building with triangles
In other words, a platonic solid is a three dimensional shape where each face is an identical flat shape with all sides and angles the same, and the same number of these faces meet at each corner.
There are 5 platonic solids, the cube (6 squares, 3 meeting at each vertex), the tetrahedron (4 triangles, 3 meeting at each vertex), the octahedron (8 triangles, 4 meeting at each vertex), the dodecahedron (12 pentagons, 3 meeting at each vertex), and the icosahedron (20 triangles, 5 meeting at each vertex).
Less able students could be supported either by help in designing the net to make a triangular prism (2 equilateral triangles joined by three squares), or they could be provided with the net to cut out, fold and stick together.
www.nzmaths.co.nz /Geometry/Shape/Buildingwithtriangles.htm   (1309 words)

  
 Polyhedron
the quasitruncated small stellated dodecahedron or small stellated truncated dodecahedron
the quasitruncated great stellated dodecahedron or great stellated truncated dodecahedron
3 have the symmetry of the snub dodecahedron:
www.majicape.com /Rol-P/Polyhedron.php   (1533 words)

  
 Untitled Document   (Site not responding. Last check: 2007-08-31)
ATH Truncated Cube 6 octagons, 8 triangles Cube
ATI Truncated Icosahedron hexagons (8,6,6) 12 pent Icosahedron
Additionally, two of the Catalan solids are edge-uniform: the rhombic dodecahedron and the rhombic triacontahedron.
www.artangent.com /sygma.htm   (488 words)

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