creates the truncated 600-cell. The truncated 120-cell or truncated hecatonicosachoron is a uniform 4-polytope, constructed by a uniform truncation of the...
12 KB (535 words) - 03:45, 4 April 2023
(600-point) 120-cell is the convex hull of 5 disjoint (120-point) 600-cells. Each (120-point) 600-cell is the convex hull of 5 disjoint (24-point) 24-cells, so...
132 KB (14,789 words) - 21:03, 24 May 2024
cantitruncated 600-cell is a uniform 4-polytope. It is composed of 1440 cells: 120 truncated icosahedra, 720 pentagonal prisms and 600 truncated octahedra. It...
15 KB (758 words) - 06:39, 13 November 2023
Bowers) The runcitruncated 120-cell or prismatorhombated hexacosichoron is a uniform 4-polytope. It contains 2640 cells: 120 truncated dodecahedra, 720 decagonal...
15 KB (707 words) - 04:32, 25 June 2023
Uniform 4-polytope (redirect from Truncated tetrahedral prism)
(star polyhedron cells and/or vertex figures) 1852: Ludwig Schläfli also found 4 of the 10 regular star 4-polytopes, discounting 6 with cells or vertex figures...
134 KB (4,310 words) - 13:51, 4 April 2024
4-polytope), which is bounded by 48 cells: 24 cubes, and 24 truncated octahedra. Each vertex joins three truncated octahedra and one cube, in an equilateral...
24 KB (1,744 words) - 03:54, 4 April 2023
which creates the truncated 16-cell. The truncated tesseract is bounded by 24 cells: 8 truncated cubes, and 16 tetrahedra. Truncated tesseract (Norman...
17 KB (1,289 words) - 21:56, 12 December 2023
polytetrahedron, being bounded by tetrahedral cells. The 600-cell's boundary is composed of 600 tetrahedral cells with 20 meeting at each vertex. Together...
217 KB (28,935 words) - 07:10, 16 May 2024
bitruncated 5-cell. The runcitruncated 5-cell or prismatorhombated pentachoron is composed of 60 vertices, 150 edges, 120 faces, and 30 cells. The cells are: 5...
40 KB (1,758 words) - 14:05, 11 October 2023
tesseract, Truncated tesseract, Cantellated tesseract, Runcinated tesseract Rectified 16-cell, Truncated 16-cell Rectified 24-cell, Truncated 24-cell, Cantellated...
47 KB (3,577 words) - 12:36, 23 May 2024
dodecahedron Archimedean solid Truncated tetrahedron, Cuboctahedron, Truncated cube, Truncated octahedron, Rhombicuboctahedron, Truncated cuboctahedron, Snub cube...
29 KB (2,667 words) - 03:43, 2 October 2023
degrees of truncations, including a bitruncation. The truncated 5-cell, truncated pentachoron or truncated 4-simplex is bounded by 10 cells: 5 tetrahedra...
21 KB (1,295 words) - 16:18, 10 May 2023
elements: vertices, edges, faces (polygons), and cells (polyhedra). Each face is shared by exactly two cells. The 4-polytopes were discovered by the Swiss...
16 KB (1,774 words) - 22:15, 5 April 2024
Runcinated tesseracts (redirect from Runcitruncated 16-cell)
the truncated cube cells project to a truncated cube in the center of the projection envelope. Six octagonal prisms connect this central truncated cube...
29 KB (2,219 words) - 04:16, 27 February 2024
plane. If the edge length of a truncated icosahedron is a, the radius of a circumscribed sphere (one that touches the truncated icosahedron at all vertices)...
17 KB (1,626 words) - 18:32, 22 May 2024
Hexagon (redirect from Truncated triangle)
the truncated tetrahedron, truncated octahedron, truncated icosahedron (of soccer ball and fullerene fame), truncated cuboctahedron and the truncated icosidodecahedron...
30 KB (2,677 words) - 19:21, 2 May 2024
In geometry, a rectified 120-cell is a uniform 4-polytope formed as the rectification of the regular 120-cell. E. L. Elte identified it in 1912 as a semiregular...
6 KB (328 words) - 09:06, 2 March 2020
rectified 600-cell or rectified hexacosichoron is a convex uniform 4-polytope composed of 600 regular octahedra and 120 icosahedra cells. Each edge has...
7 KB (492 words) - 09:06, 2 March 2020
Chamfer (geometry) (redirect from Alternate truncated cube)
.. The truncated octahedron or truncated icosahedron, GP(1,1), creates a Goldberg sequence: GP(1,1), GP(2,2), GP(4,4), GP(8,8)... A truncated tetrakis...
25 KB (1,263 words) - 02:05, 25 May 2024
24-cells inscribed in the 120-cell, a regular 4-polytope with 120 dodecahedral cells that is the convex hull of the compound of 25 disjoint 24-cells. Perez-Gracia...
237 KB (31,111 words) - 22:10, 24 May 2024
Uniform polytope (section Truncated forms)
Faces are truncated, doubling their edges. (The term, coined by Kepler, comes from Latin truncare 'to cut off'.) There are higher truncations also: bitruncation...
53 KB (2,947 words) - 14:31, 6 November 2023
consisting of 120 regular dodecahedron cells. It also has 120 disjoint regular 5-cells inscribed in it. These are not 3-dimensional cells but 4-dimensional...
48 KB (5,298 words) - 18:12, 21 May 2024
Uniform 5-polytope (redirect from 120-cell prism)
24-cell honeycomb, with symbols {3,4,3,3}, . There are 31 reflective uniform honeycombs in this family, and one alternated form. Truncated 24-cell honeycomb...
92 KB (2,241 words) - 15:03, 6 April 2024
the snub 24-cell or snub disicositetrachoron is a convex uniform 4-polytope composed of 120 regular tetrahedral and 24 icosahedral cells. Five tetrahedra...
19 KB (1,780 words) - 02:03, 6 May 2024
Icosahedral honeycomb (redirect from Truncated icosahedral honeycomb)
regular honeycombs: The truncated icosahedral honeycomb, t0,1{3,5,3}, , has alternating dodecahedron and truncated icosahedron cells, with a triangular pyramid...
19 KB (700 words) - 02:01, 20 January 2024
vertex figure: two hexagonal prisms, and two truncated cuboctahedra. The 48 truncated cuboctahedral cells are joined to each other via their octagonal...
17 KB (1,115 words) - 15:49, 7 October 2022
Hexagonal tiling honeycomb (redirect from Truncated triangular tiling honeycomb)
triangular prism cells, with a wedge vertex figure. The cantitruncated hexagonal tiling honeycomb, t0,1,2{6,3,3}, has truncated tetrahedron, truncated trihexagonal...
21 KB (843 words) - 18:07, 31 December 2023
Order-5 cubic honeycomb (redirect from Truncated order-5 cubic honeycomb)
Schläfli symbol h2,3{4,3,5}. It has truncated dodecahedron, truncated icosidodecahedron, and truncated tetrahedron cells, with an irregular tetrahedron vertex...
22 KB (844 words) - 01:02, 23 February 2024
there are 15 uniform polytopes with H4 symmetry. Two of these, the 120-cell and 600-cell, are regular. Each can be visualized as symmetric orthographic projections...
14 KB (469 words) - 23:13, 26 March 2024
located inside the cubic cells of the 7-cube. The final three truncations are best expressed relative to the 7-orthoplex. Truncated hepteract (Jonathan Bowers)...
7 KB (358 words) - 19:40, 9 April 2024