*  Order-6 cubic honeycomb - Wikipedia
The rectified order-6 cubic honeycomb, r{4,3,6}, has cuboctahedral and triangular tiling facets, with a hexagonal prism vertex ... It in a sequence of regular polychora and honeycombs with cubic cells. It a part of a sequence of honeycombs with triangular ... with a triangular prism vertex figure. In 3-dimensional hyperbolic geometry, the alternated order-6 hexagonal tiling honeycomb ... Its vertex figure is an infinite triangular tiling. It is dual is the order-4 hexagonal tiling honeycomb. A geometric honeycomb ...
  https://en.wikipedia.org/wiki/Order-6_cubic_honeycomb
*  Order-6 tetrahedral honeycomb - Wikipedia
... has truncated tetrahedra and triangular tiling cells connected in a hexagonal prism vertex figure. The cantellated order-6 ... It a part of a sequence of honeycombs with triangular tiling vertex figures. The rectified order-6 tetrahedral honeycomb, t1{3, ... All vertices are ideal vertices with infinitely many tetrahedra existing around each ideal vertex in an triangular tiling ... 3,6} has octahedral and triangular tiling cells connected in a hexagonal prism vertex figure. Perspective projection view ...
  https://en.wikipedia.org/wiki/Order-6_tetrahedral_honeycomb
*  Order-6 dodecahedral honeycomb - Wikipedia
... has icosidodecahedron and triangular tiling cells connected in a hexagonal prism vertex figure. Perspective projection view ... order-5 hexagonal tiling honeycomb, {6,3,5}. This honeycomb is a part of a sequence of polychora and honeycombs with triangular ... Each vertex is ideal and surrounded by infinitely many dodecahedra with a vertex figure as a triangular tiling. A geometric ... has truncated dodecahedron and triangular tiling cells connected in a hexagonal pyramid vertex figure. The cantellated order-6 ...
  https://en.wikipedia.org/wiki/Order-6_dodecahedral_honeycomb
*  Order-4 hexagonal tiling honeycomb - Wikipedia
... with a triangular prism vertex figure. The runcinated order-4 hexagonal tiling honeycomb, t0,3{6,3,4}, has cube, hexagonal ... having triangular tiling and octahedron cells. It is a part of sequence of regular honeycombs with hexagonal tiling cells of ... with a tetrahedron vertex figure. The quarter order-4 hexagonal tiling honeycomb, q{6,3,4}, or with a triangular cupola vertex ... tiling and hexagonal prism cells, with a triangular antiprism vertex figure. It contains the 2D hyperbolic rhombitetrahexagonal ...
  https://en.wikipedia.org/wiki/Order-4_hexagonal_tiling_honeycomb
*  Prism graph - Wikipedia
6 vertices, 9 edges Cubical graph - 8 vertices, 12 edges Pentagonal prism graph - 10 vertices, 15 edges Hexagonal prism graph ... the graphs of these star prisms are isomorphic to the prism graphs, and do not form a separate sequence of graphs. Prism graphs ... The pentagonal prism is one of the forbidden minors for the graphs of treewidth three. The triangular prism and cube graph have ... Since the prism has symmetries taking each vertex to each other vertex, the prism graphs are vertex-transitive graphs. As ...
  https://en.wikipedia.org/wiki/Prism_graph
*  Hexagonal tiling honeycomb - Wikipedia
Triangular prism, Dodecagonal prism, and truncated hexagonal tiling cells, with a quad-pyramid vertex figure. The ... It is a part of sequence of regular honeycombs of the form {6,3,p}, with hexagonal tiling cells: The rectified hexagonal tiling ... rhombitrihexagonal tiling hexagonal prism, triangular prism cells, with a octahedron vertex figure. The runcitruncated ... hexagonal prism, hexagonal prism, and rhombitrihexagonal tiling cells, with a quad-pyramid vertex figure. The omnitruncated ...
  https://en.wikipedia.org/wiki/Hexagonal_tiling_honeycomb
*  Triangular prism - Wikipedia
This polyhedron is topologically related as a part of sequence of cantellated polyhedra with vertex figure (3.4.n.4), and ... snub triangular-hexagonal prismatic honeycomb, elongated triangular prismatic honeycomb The triangular prism is first in a ... A right triangular prism has rectangular sides, otherwise it is oblique. A uniform triangular prism is a right triangular prism ... There are 4 uniform compounds of triangular prisms: Compound of four triangular prisms, compound of eight triangular prisms, ...
  https://en.wikipedia.org/wiki/Triangular_prism
*  Order-5 hexagonal tiling honeycomb - Wikipedia
... with a triangular prism vertex figure. The bitruncated order-5 hexagonal tiling honeycomb, t1,2{6,3,5}, has a tetrahedral ... having icosahedron and triangular tiling cells. It is a part of sequence of regular honeycombs with hexagonal tiling hyperbolic ... with a triangular antiprism vertex figure. The runcitruncated order-5 hexagonal tiling honeycomb, t0,1,3{6,3,5}, has a ... has icosahedron and triangular tiling facets, with a pentagonal pyramid vertex figure. The cantellated order-5 hexagonal tiling ...
  https://en.wikipedia.org/wiki/Order-5_hexagonal_tiling_honeycomb
*  Cube - Wikipedia
The cube is a square prism: As a trigonal trapezohedron, the cube is related to the hexagonal dihedral symmetry family. It is ... A cube can be inscribed in a dodecahedron so that each vertex of the cube is a vertex of the dodecahedron and each edge is a ... The cube is a part of a sequence of rhombic polyhedra and tilings with [n,3] Coxeter group symmetry. The cube can be seen as a ... If smaller corners are cut off we get a polyhedron with six octagonal faces and eight triangular ones. In particular we can get ...
  https://en.wikipedia.org/wiki/Cube
*  Prism (geometry) - Wikipedia
... snub triangular-hexagonal prismatic honeycomb, elongated triangular prismatic honeycomb. The triangular prism is first in a ... This polyhedron is topologically related as a part of sequence of cantellated polyhedra with vertex figure (3.4.n.4), and ... There are 4 uniform compounds of triangular prisms: Compound of four triangular prisms, compound of eight triangular prisms, ... compound of ten triangular prisms, compound of twenty triangular prisms. There are 9 uniform honeycombs that include triangular ...
  https://en.wikipedia.org/wiki/Prism_(geometry)
*  Hexagonal prism - Wikipedia
This polyhedron can be considered a member of a sequence of uniform patterns with vertex figure (4.6.2p) and Coxeter-Dynkin ... However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces. Because of ... In geometry, the hexagonal prism is a prism with hexagonal base. This polyhedron has 8 faces, 18 edges, and 12 vertices. Since ... The dual of a hexagonal prism is a hexagonal bipyramid. The symmetry group of a right hexagonal prism is D6h of order 24. The ...
  https://en.wikipedia.org/wiki/Hexagonal_prism
*  Octahedron - Wikipedia
They all have six vertices, eight triangular faces, and twelve edges that correspond one-for-one with the features of a regular ... Hexagonal prism: Two faces are parallel regular hexagons; six squares link corresponding pairs of hexagon edges. Heptagonal ... The octahedron as a tetratetrahedron exists in a sequence of symmetries of quasiregular polyhedra and tilings with vertex ... There are 3 uniform colorings of the octahedron, named by the triangular face colors going around each vertex: 1212, 1112, 1111 ...
  https://en.wikipedia.org/wiki/Octahedron
*  Gyrobifastigium - Wikipedia
... triangular and hexagonal prism) and it is the only Johnson solid capable of doing so. The following formulae for volume and ... Just as the other regular cupolas have an alternating sequence of squares and triangles surrounding a single polygon at the top ... These polyhedra resemble the dual gyrobifastigium in that both shapes have eight vertices and eight faces, with the faces ... The related elongated digonal gyrobicupola is formed by augmenting two triangular prisms to a central cube. The elongated ...
  https://en.wikipedia.org/wiki/Gyrobifastigium
*  Truncated cuboctahedron - Wikipedia
It has 12 square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices and 72 edges. Since each of its faces ... This polyhedron can be considered a member of a sequence of uniform patterns with vertex configuration (4.6.2p) and Coxeter- ... 8 triangular cupolas above each triangular face, and 12 cubes above the secondary square faces. A dissected truncated ... The truncated cuboctahedron can tessellate with the octagonal prism. Alternate interchangeable names are: Truncated ...
  https://en.wikipedia.org/wiki/Truncated_cuboctahedron
*  Chamfer (geometry) - Wikipedia
... containing triangular and hexagonal faces. It can look a little like a truncated tetrahedron, , which has 4 hexagonal and 4 ... The original 12 rhombic faces become flattened hexagons, and the truncated vertices become squares. The hexagonal faces are ... The chamfer operator transforms GP(m,n) to GP(2m,2n). A regular polyhedron, GP(1,0), create a Goldberg polyhedra sequence: GP(1 ... For polychora, new cells are created around the original edges, The cells are prisms, containing two copies of the original ...
  https://en.wikipedia.org/wiki/Chamfer_(geometry)
*  Order-6 hexagonal tiling honeycomb - Wikipedia
... has hexagonal tiling and hexagonal prism cells, with a triangular antiprism vertex figure. It is analogous to the 2D hyperbolic ... This honeycomb is a part of a sequence of polychora and honeycombs with triangular tiling vertex figures: The rectified order-6 ... with a triangular prism vertex figure. The cantitruncated order-6 hexagonal tiling honeycomb, t0,1,2{6,3,6}, has hexagonal ... with a triangular prism vertex figure. The runcinated order-6 hexagonal tiling honeycomb, t0,3{6,3,6}, ...
  https://en.wikipedia.org/wiki/Order-6_hexagonal_tiling_honeycomb
*  Rhombic dodecahedron - Wikipedia
... bees use the geometry of rhombic dodecahedra to form honeycombs from a tessellation of cells each of which is a hexagonal prism ... The triangular faces of each pair of adjacent pyramids lie on the same plane, and so merge into rhombuses. The 24-cell may also ... The eight vertices where three faces meet at their obtuse angles have Cartesian coordinates: (±1, ±1, ±1) The coordinates of ... This polyhedron is a part of a sequence of rhombic polyhedra and tilings with [n,3] Coxeter group symmetry. The cube can be ...
  https://en.wikipedia.org/wiki/Rhombic_dodecahedron
*  Order-4 dodecahedral honeycomb - Wikipedia
... with a triangular prism vertex figure. The cantitruncated order-4 dodecahedral honeycomb, is a uniform honeycomb constructed ... and order-4 hexagonal tiling honeycomb all which have octahedral vertex figures: This honeycomb is a part of a sequence of ... and 8 dodecahedra around each vertex in an octahedral arrangement. Its vertices are constructed from 3 orthogonal axes. Its ... It a half symmetry construction, {5,31,1}, with two types (colors) of hexagonal tilings in the Wythoff construction. ↔ . ...
  https://en.wikipedia.org/wiki/Order-4_dodecahedral_honeycomb
*  Icosahedral honeycomb - Wikipedia
... hexagonal prism and triangular prism cells, with a square pyramid vertex figure. Viewed from center of triangular prism The ... There are four regular compact honeycombs in 3D hyperbolic space: It a part of a sequence of regular polychora and honeycombs { ... triangular prism and hexagonal prism cells, with a mirrored sphenoid vertex figure. The runcinated icosahedral honeycomb, t0,3{ ... has icosahedron and triangular prism cells, with a pentagonal antiprism vertex figure. Viewed from center of triangular prism ...
  https://en.wikipedia.org/wiki/Icosahedral_honeycomb
*  Informatics | Free Full-Text | Supporting Sensemaking of Complex Objects with Visualizations: Visibility and Complementarity...
How are the 4 types of cells (i.e., Truncated Cuboctahedron, Octagonal Prism, Hexagonal Prism, and Truncated Octahedron) ... Compare the Triangular Prisms and the Truncated Tetrahedra. What common features join them in the polytope? ... From a top-down view, activities can be broken down into a sequence of tasks, and tasks can be broken down into a sequence of ... For instance, a dodecacontachoron (see Figure 2b), which is only moderate in complexity, contains 600 vertices, 1200 edges, 720 ...
  http://mdpi.com/2227-9709/3/4/20/htm
*  Skew apeirogon - Wikipedia
This apeirogon can be most seen as constructed from the vertices in an infinite stack of uniform n-gonal uniform prisms or ... between pairs of hexagonal and pairs of triangular faces: Coxeter, H. S. M. and Moser, W. O. J. (1980), p.54 5.2 The Petrie ... A sequence of edges of a Boerdijk-Coxeter helix can represent regular helical apeirogons with an irrational twist angle: A ... here for example with square prisms, alternating red and blue edges: Similarly an alternating stack of prisms and antiprisms ...
  https://en.wikipedia.org/wiki/Skew_apeirogon
*  Interesting Things For you Late @ Night: 03/15/08
... is an hexagonal prism number.1354 has a 5th power that is closer to a cube than a square.1357 has digits in arithmetic sequence ... 111111111 in base 3.9843 is the number of vertices in a Sierpinski triangle of order 8.9854 is the index of a triangular number ... 8.9451 is the number of binary rooted trees with 19 vertices.9455 is the sum of the first 30 squares.9465 is an hexagonal prism ... vertices.303 has a cube that is a concatenation of other cubes.304 is a primitive semiperfect number.305 is an hexagonal prism ...
  http://yayyuh.blogspot.com/2008_03_15_archive.html
*  Complex polytope - Wikipedia
2{4}2, or , with 4 vertices, and 4 2-edges 3{4}2, or , with 9 vertices, and 6 (triangular) 3-edges 4{4}2, or , with 16 vertices ... with 36 vertices, and 12 (hexagonal) 6-edges 4{4}2, or , with 49 vertices, and 14 (heptagonal)7-edges 4{4}2, or , with 64 ... While 1-polytopes can have unlimited p, finite regular complex polygons, excluding the double prism polygons p{4}2, are limited ... in the sense that one can get from any member of this set to any other by a sequence of containments; and the subset of unitary ...
  https://en.wikipedia.org/wiki/Complex_polytope
*  Square tiling honeycomb - Wikipedia
... triangular prism, cube, and square tiling facets, with a triangular antiprism vertex figure. The runcitruncated square tiling ... hexagonal prism, octagonal prism facets, with a tetrahedron vertex figure. The alternated omnitruncated square tiling honeycomb ... with a cubic vertex figure. It is a part of a sequence of honeycombs with square tiling cells: The rectified square tiling ... The cantellated square tiling honeycomb, rr{4,4,3}, has cube and truncated square tiling facets, with a triangular prism vertex ...
  https://en.wikipedia.org/wiki/Square_tiling_honeycomb
*  5-cell - Wikipedia
... and its vertex figure is a tetrahedron. Its maximal intersection with 3-dimensional space is the triangular prism. Its dihedral ... It is in the sequence of regular polychora: the tesseract {4,3,3}, 120-cell {5,3,3}, of Euclidean 4-space, and hexagonal tiling ... The 10 triangle faces can be seen in a 2D net within a triangular tiling, with 6 triangles around every vertex, although ... Many uniform 5-polytopes have tetrahedral pyramid vertex figures: Other uniform 5-polytopes have irregular 5-cell vertex ...
  https://en.wikipedia.org/wiki/5-cell