Schlegel diagram
Type	Prismatic uniform polychoron
Uniform index	54
Schläfli symbol	t0,1{3,4}×{} t0,1,2{3,3}×{}
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	|16: 2 3.6.6 Truncated tetrahedron In geometry, the truncated tetrahedron is an Archimedean solid. It has 4 regular hexagonal faces, 4 regular triangular faces, 12 vertices and 18 edges.- Area and volume :... 6 {4,3} 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 {}x{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...
Faces	64: 48 {4} Square (geometry) In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles... 16 {6}
Edges	96
Vertices	48
Vertex configuration	Isosceles-triangular pyramid
Symmetry group Coxeter notation In geometry, Coxeter notation is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group. It uses a bracketed notation, with modifiers to indicate certain subgroups. The notation is named after H. S. M...	[3,4,2], order 96 [3,3,2], order 48
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 4-dimensional 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 octahedral 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). This polychoron has 16 cell

Cell (geometry)

In geometry, a cell is a three-dimensional element that is part of a higher-dimensional object.- In polytopes :A cell is a three-dimensional polyhedron element that is part of the boundary of a higher-dimensional polytope, such as a polychoron or honeycomb For example, a cubic honeycomb is made...

s (2 truncated octahedra

Truncated octahedron

In geometry, the truncated octahedron is an Archimedean solid. It has 14 faces , 36 edges, and 24 vertices. Since each of its faces has point symmetry the truncated octahedron is a zonohedron....

 connected by 6 cube

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...

s, 8 hexagonal prism

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...

s.) It has 64 faces (48 squares

Square (geometry)

In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...

 and 16 hexagons), and 96 edges and 48 vertices.

It has two symmetry constructions, one from the truncated

Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.- Uniform truncation :...

 octahedron

Octahedron

In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex....

, and one as an omnitruncation of the 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...

.

Alternative names:

1. Truncated-octahedral dyadic prism (Norman W. Johnson)
2. Truncated octahedral hyperprism
3. Tope (Jonathan Bowers: for truncated-octahedral prism)

It is one of 18 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 parallel 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 and 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.