hyperbolic 3-space, the order-3-6 heptagonal honeycomb a regular space-filling tessellation (or honeycomb). Each infinite cell consists of a heptagonal tiling...
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honeycomb is a heptagonal tiling, {∞,3}. In the geometry of hyperbolic 3-space, the order-infinite-3 hexagonal honeycomb (or 6,∞,3 honeycomb) a regular space-filling...
31 KB (1,578 words) - 00:14, 28 January 2024
regular honeycombs with order-7 triangular tiling cells: {3,7,p}. It isa part of a sequence of regular honeycombs with heptagonal tiling vertex figures:...
25 KB (1,299 words) - 00:14, 28 January 2024
geometry of hyperbolic 3-space, the heptagonal tiling honeycomb or 7,3,3 honeycomb a regular space-filling tessellation (or honeycomb). Each infinite cell...
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of the order-5-3 heptagonal honeycomb is {7,5,3}, with three order-5 heptagonal tilings meeting at each edge. The vertex figure of this honeycomb is a dodecahedron...
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of the order-4-3 heptagonal honeycomb is {7,4,3}, with three order-4 heptagonal tilings meeting at each edge. The vertex figure of this honeycomb is a cube...
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Hosohedron (redirect from Order-2 heptagonal hosohedral honeycomb)
C_{nv}} , [ n ] {\displaystyle [n]} , ( ∗ n n ) {\displaystyle (*nn)} , order 2 n {\displaystyle 2n} . The reflection domains can be shown by alternately...
8 KB (592 words) - 20:45, 25 January 2023
symmetry is [6,5,6,1+] = [6,((5,3,5))]. In the geometry of hyperbolic 3-space, the order-5-7 heptagonal honeycomb (or 7,5,7 honeycomb) is a regular space-filling...
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Euclidean 3-space, yielding the small cubicuboctahedron. The dual order-3 heptagonal tiling has the same symmetry group, and thus yields heptagonal tilings...
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of sequence of regular tilings with heptagonal faces, starting with the heptagonal tiling, with Schläfli symbol {6,n}, and Coxeter diagram , progressing...
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constructed in 3-space. The dual tiling is called a heptakis heptagonal tiling, named for being constructible as a heptagonal tiling with every heptagon divided...
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List of regular polytopes (redirect from Order-3 120-cell honeycomb)
constraints allow for 21 forms: 6 are convex, 10 are nonconvex, one is a Euclidean 3-space honeycomb, and 4 are hyperbolic honeycombs. The Euler characteristic...
97 KB (5,294 words) - 07:52, 5 July 2024
600-cell (redirect from Order-3-5 triangular honeycomb)
5-cell {3,3,3}, 16-cell {3,3,4} of Euclidean 4-space, and the order-6 tetrahedral honeycomb {3,3,6} of hyperbolic space. All of these have tetrahedral cells...
217 KB (28,935 words) - 07:10, 16 May 2024
dodecahedral honeycomb Weaire–Phelan structure Convex uniform honeycombs in hyperbolic space Order-4 dodecahedral honeycomb Order-5 cubic honeycomb Order-5 dodecahedral...
29 KB (2,667 words) - 01:10, 4 June 2024
geometry, a heptagonal tiling is a regular tiling of the hyperbolic plane. It is represented by Schläfli symbol of {7,3}, having three regular heptagons around...
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Triheptagonal tiling (redirect from Order-7-3 rhombille tiling)
hyperbolic plane, representing a rectified Order-3 heptagonal tiling. There are two triangles and two heptagons alternating on each vertex. It has Schläfli...
3 KB (262 words) - 21:57, 12 December 2023
Octahedron (redirect from Order-4 triangular tiling)
six squares link corresponding pairs of hexagon edges. Heptagonal pyramid: One face is a heptagon (usually regular), and the remaining seven faces are triangles...
26 KB (2,764 words) - 20:47, 29 May 2024
List of mathematical shapes (section Honeycombs)
honeycomb Order-4 dodecahedral honeycomb Order-5 dodecahedral honeycomb Order-5 cubic honeycomb Icosahedral honeycomb Order-3 icosahedral honeycomb Order-4...
47 KB (3,580 words) - 17:01, 29 June 2024
In geometry, the truncated order-4 heptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{7,4}. There are two uniform...
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120-cell (redirect from Order-3-3 pentagonal honeycomb)
and tesseract {4,3,3} of Euclidean 4-space, and the hexagonal tiling honeycomb {6,3,3} of hyperbolic space. All of these have a tetrahedral vertex figure...
132 KB (14,816 words) - 06:13, 20 June 2024
Snub triheptagonal tiling (redirect from Snub order-3 heptagonal tiling)
geometry, the order-3 snub heptagonal tiling is a semiregular tiling of the hyperbolic plane. There are four triangles and one heptagon on each vertex...
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Duoprism (redirect from 3-6 duoprism)
5-simplex. The fourth figure is a Euclidean honeycomb, 222, and the final is a paracompact hyperbolic honeycomb, 322, with Coxeter group [32,2,3], T ¯ 7...
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In geometry, the truncated heptagonal tiling is a semiregular tiling of the hyperbolic plane. There are one triangle and two tetradecagons on each vertex...
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Quasiregular polyhedron (redirect from Quasiregular honeycomb)
vertex figure (3.7)2 - a quasiregular tiling based on the order-7 triangular tiling and heptagonal tiling. Coxeter, H.S.M. et al. (1954) also classify certain...
30 KB (1,484 words) - 18:07, 31 December 2023
with the order-5 5-cell honeycomb and the order-5 120-cell honeycomb, both of which have five cells around each face. Compact hyperbolic honeycombs only exist...
104 KB (13,347 words) - 06:21, 5 July 2024
tiling honeycomb, h{6,3,3}, . It is also constructed as s{3[3,3]} and . Another hyperbolic (scaliform) honeycomb is a snub order-4 octahedral honeycomb, s{3...
25 KB (1,424 words) - 16:35, 5 June 2024
number, the third hexagonal pyramidal number, and the third centered heptagonal number, the number of partitions of 8, as well as the sum of the totient...
30 KB (3,624 words) - 19:30, 22 June 2024
the regular order-7 triangular tiling, {3,7}. The full set of edges coincide with the edges of a heptakis heptagonal tiling. The valance 6 vertices in...
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2 points of an 8 × 8 grid of points 939 = 3 × 313, number of V-toothpicks after 31 rounds of the honeycomb sequence 940 = 22 × 5 × 47, totient sum for...
29 KB (3,815 words) - 16:07, 7 July 2024
{\displaystyle \mathbb {C} ^{2}} and 1 in C 3 {\displaystyle \mathbb {C} ^{3}} . 11 regular paracompact hyperbolic honeycombs with infinite facets and vertex figures...
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