##### Order-6 cubic honeycomb - Wikipedia

The rectified order-6 cubic honeycomb, r{4,3,6}, has cuboctahedral and

https://en.wikipedia.org/wiki/Order-6_cubic_honeycomb**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 ...##### Order-6 tetrahedral honeycomb - Wikipedia

... has truncated tetrahedra and

https://en.wikipedia.org/wiki/Order-6_tetrahedral_honeycomb**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 ...##### Order-6 dodecahedral honeycomb - Wikipedia

... has icosidodecahedron and

https://en.wikipedia.org/wiki/Order-6_dodecahedral_honeycomb**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 ...##### Order-4 **hexagonal** tiling honeycomb - Wikipedia

... with a

https://en.wikipedia.org/wiki/Order-4_hexagonal_tiling_honeycomb**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 ...##### **Prism** graph - Wikipedia

6

https://en.wikipedia.org/wiki/Prism_graph**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 ...##### **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 ...

##### **Triangular** **prism** - Wikipedia

This polyhedron is topologically related as a part of

https://en.wikipedia.org/wiki/Triangular_prism**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**, ...##### Order-5 **hexagonal** tiling honeycomb - Wikipedia

... with a

https://en.wikipedia.org/wiki/Order-5_hexagonal_tiling_honeycomb**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 ...##### **Prism** (geometry) - Wikipedia

... snub

https://en.wikipedia.org/wiki/Prism_(geometry)**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**...##### Cube - Wikipedia

The cube is a square

https://en.wikipedia.org/wiki/Cube**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 ...##### **Hexagonal** **prism** - Wikipedia

This polyhedron can be considered a member of a

https://en.wikipedia.org/wiki/Hexagonal_prism**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 ...##### Octahedron - Wikipedia

They all have six

https://en.wikipedia.org/wiki/Octahedron**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 ...##### Gyrobifastigium - Wikipedia

...

https://en.wikipedia.org/wiki/Gyrobifastigium**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 ...##### Truncated cuboctahedron - Wikipedia

It has 12 square faces, 8 regular

https://en.wikipedia.org/wiki/Truncated_cuboctahedron**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 ...##### Chamfer (geometry) - Wikipedia

... containing

https://en.wikipedia.org/wiki/Chamfer_(geometry)**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 ...##### Order-6 **hexagonal** tiling honeycomb - Wikipedia

... has

https://en.wikipedia.org/wiki/Order-6_hexagonal_tiling_honeycomb**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}, ...##### Rhombic dodecahedron - Wikipedia

... bees use the geometry of rhombic dodecahedra to form honeycombs from a tessellation of cells each of which is a

https://en.wikipedia.org/wiki/Rhombic_dodecahedron**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 ...##### Order-4 dodecahedral honeycomb - Wikipedia

... with a

https://en.wikipedia.org/wiki/Order-4_dodecahedral_honeycomb**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. ↔ . ...##### Icosahedral honeycomb - Wikipedia

...

https://en.wikipedia.org/wiki/Icosahedral_honeycomb**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**...##### Skew apeirogon - Wikipedia

This apeirogon can be most seen as constructed from the

https://en.wikipedia.org/wiki/Skew_apeirogon**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 ...##### Square tiling honeycomb - Wikipedia

...

https://en.wikipedia.org/wiki/Square_tiling_honeycomb**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**...##### Complex polytope - Wikipedia

2{4}2, or , with 4

https://en.wikipedia.org/wiki/Complex_polytope**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 ...##### Interesting Things For you Late @ Night: 03/15/08

... is an

http://yayyuh.blogspot.com/2008_03_15_archive.html**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**...##### 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

http://mdpi.com/2227-9709/3/4/20/htm**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 ...##### 5-cell - Wikipedia

... and its

https://en.wikipedia.org/wiki/5-cell**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**...