Truncated cuboctahedral prism
Encyclopedia

Schlegel diagram
Type Prismatic uniform polychoron
Uniform index 55
Schläfli symbol t0,1,2{4,3}x{}
Coxeter-Dynkin
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...

Cells 28 total:

2
4.6.8
Truncated cuboctahedron
In geometry, the truncated cuboctahedron is an Archimedean solid. It has 12 square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices and 72 edges...



12 4.4.4
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...



8 4.4.6
Hexagonal prism
In geometry, the hexagonal prism is a prism with hexagonal base. The shape has 8 faces, 18 edges, and 12 vertices.Since it has eight faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces...



6 4.4.8
Octagonal prism
In geometry, the octagonal prism is the sixth in an infinite set of prisms, formed by square sides and two regular octagon caps.If faces are all regular, it is a semiregular polyhedron.- Use :...

Faces 124 total:

96 {4}

16 {6}

12 {8}
Edges 192
Vertices 96
Vertex figure irr. tetrahedron
Tetrahedron
In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...

Symmetry group
Symmetry group
The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...

[4,3,2], order 96
Properties convex
Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn...



In geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, a truncated cuboctahedral prism is a convex uniform
Uniform polychoron
In geometry, a uniform polychoron is a polychoron or 4-polytope which is vertex-transitive and whose cells are uniform polyhedra....

 polychoron
Polychoron
In geometry, a polychoron or 4-polytope is a four-dimensional polytope. It is a connected and closed figure, composed of lower dimensional polytopal elements: vertices, edges, faces , and cells...

 (four dimensional polytope
Polytope
In elementary geometry, a polytope is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions, a polyhedron in three dimensions, and so on in higher dimensions...

).

It is one of 18 convex uniform polyhedral prisms created by using uniform prism
Prism (geometry)
In geometry, a prism is a polyhedron with an n-sided polygonal base, a translated copy , and n other faces joining corresponding sides of the two bases. All cross-sections parallel to the base faces are the same. Prisms are named for their base, so a prism with a pentagonal base is called a...

s to connect pairs of Platonic solid
Platonic solid
In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and...

s or Archimedean solid
Archimedean solid
In geometry an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices...

s in parallel hyperplane
Hyperplane
A hyperplane is a concept in geometry. It is a generalization of the plane into a different number of dimensions.A hyperplane of an n-dimensional space is a flat subset with dimension n − 1...

s.

Alternative names

  • Truncated-cuboctahedral dyadic prism (Norman W. Johnson)
  • Gircope (Jonathan Bowers: for great-rhombicuboctahedral prism)
  • Truncated-cuboctahedral hyperprism
  • Great-rhombicuboctahedral prism
  • Great-rhombicuboctahedral hyperprism
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