hyperbolic 3-space, the order-3-6 heptagonal honeycomb a regular space-filling tessellation (or honeycomb). Each infinite cell consists of a heptagonal tiling...

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...

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:...

geometry of hyperbolic 3-space, the heptagonal tiling honeycomb or 7,3,3 honeycomb a regular space-filling tessellation (or honeycomb). Each infinite cell...

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...

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...

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...

C_{nv}} , [ n ] {\displaystyle [n]} , ( ∗ n n ) {\displaystyle (*nn)} , order 2 n {\displaystyle 2n} . The reflection domains can be shown by alternately...

Euclidean 3-space, yielding the small cubicuboctahedron. The dual order-3 heptagonal tiling has the same symmetry group, and thus yields heptagonal tilings...

of sequence of regular tilings with heptagonal faces, starting with the heptagonal tiling, with Schläfli symbol {6,n}, and Coxeter diagram , progressing...

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...

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...

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...

dodecahedral honeycomb Weaire–Phelan structure Convex uniform honeycombs in hyperbolic space Order-4 dodecahedral honeycomb Order-5 cubic honeycomb Order-5 dodecahedral...

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...

hyperbolic plane, representing a rectified Order-3 heptagonal tiling. There are two triangles and two heptagons alternating on each vertex. It has Schläfli...

honeycomb Order-4 dodecahedral honeycomb Order-5 dodecahedral honeycomb Order-5 cubic honeycomb Icosahedral honeycomb Order-3 icosahedral honeycomb Order-4...

six squares link corresponding pairs of hexagon edges. Heptagonal pyramid: One face is a heptagon (usually regular), and the remaining seven faces are triangles...

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...

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...

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...

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...

In geometry, the truncated heptagonal tiling is a semiregular tiling of the hyperbolic plane. There are one triangle and two tetradecagons on each vertex...

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...

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...

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...

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...

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...

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...

{\displaystyle \mathbb {C} ^{2}} and 1 in C 3 {\displaystyle \mathbb {C} ^{3}} . 11 regular paracompact hyperbolic honeycombs with infinite facets and vertex figures...