Truncated hexagonal prismatic honeycomb
Encyclopedia
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| Type | Uniform honeycomb Convex uniform honeycomb In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.Twenty-eight such honeycombs exist:* the familiar cubic honeycomb and 7 truncations thereof;... |
| Schläfli symbol | t0,1{6,3} x {∞} |
| Coxeter-Dynkin diagram Coxeter-Dynkin diagram In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors... |
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| Cell types | 4.4.12 Dodecagonal prism In geometry, the dodecagonal prism is the tenth in an infinite set of prisms, formed by square sides and two regular dodecagon caps.If faces are all regular, it is a semiregular polyhedron.- Use :...  3.4.4 Triangular prism In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides....  |
| Face types | {3} Triangle A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted .... , {4} Square (geometry) In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles... , {12} Dodecagon In geometry, a dodecagon is any polygon with twelve sides and twelve angles.- Regular dodecagon :It usually refers to a regular dodecagon, having all sides of equal length and all angles equal to 150°... |
| Edge figures | Square Square (geometry) In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles... , Isosceles triangle |
| Vertex figure | Triangular bipyramid |
| Cells/edges | (4.4.12) Dodecagonal prism In geometry, the dodecagonal prism is the tenth in an infinite set of prisms, formed by square sides and two regular dodecagon caps.If faces are all regular, it is a semiregular polyhedron.- Use :... 2.(3.4.4) Triangular prism In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.... (4.4.12) Dodecagonal prism In geometry, the dodecagonal prism is the tenth in an infinite set of prisms, formed by square sides and two regular dodecagon caps.If faces are all regular, it is a semiregular polyhedron.- Use :... 2.(3.4.4) Triangular prism In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.... 2 (4.4.12) Dodecagonal prism In geometry, the dodecagonal prism is the tenth in an infinite set of prisms, formed by square sides and two regular dodecagon caps.If faces are all regular, it is a semiregular polyhedron.- Use :... 4 |
| Faces/edges | {3}.{4}.{12}.{4} {4}3 {4}4 |
| Cells/vertex | 4 (4.4.12) Dodecagonal prism In geometry, the dodecagonal prism is the tenth in an infinite set of prisms, formed by square sides and two regular dodecagon caps.If faces are all regular, it is a semiregular polyhedron.- Use :... + 2 (3.4.4) Triangular prism In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.... |
| Faces/vertex | 1 {3}, 3 {4}, 2 {12} |
| Edges/vertex | 5 |
| Coxeter group Coxeter group In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example... |
[6,3]x[∞] |
| Dual | ? |
| Properties | vertex-transitive Vertex-transitive In geometry, a polytope is isogonal or vertex-transitive if, loosely speaking, all its vertices are the same... |
The truncated hexagonal prismatic honeycomb is a space-filling tessellation
Tessellation
A tessellation or tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art...
(or honeycomb
Honeycomb (geometry)
In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions....
) in Euclidean 3-space. It is composed of dodecagonal prism
Dodecagonal prism
In geometry, the dodecagonal prism is the tenth in an infinite set of prisms, formed by square sides and two regular dodecagon caps.If faces are all regular, it is a semiregular polyhedron.- Use :...
s, and triangular prism
Triangular prism
In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides....
s in a ratio of 1:2.
It is constructed from a truncated hexagonal tiling
Truncated hexagonal tiling
In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane. There are 2 dodecagons and one triangle on each vertex....
extruded into prisms.
It is one of 28 convex uniform honeycomb
Convex uniform honeycomb
In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.Twenty-eight such honeycombs exist:* the familiar cubic honeycomb and 7 truncations thereof;...
s.