Truncated 5-orthoplex

Orthogonal projections in BC₅ Coxeter plane
5-orthoplex	Truncated 5-orthoplex	Bitruncated 5-orthoplex
5-cube	Truncated 5-cube Truncated 5-cube In five-dimensional geometry, a truncated 5-cube is a convex uniform 5-polytope, being a truncation of the regular 5-cube.There are four unique truncations of the 5-cube. Vertices of the truncated 5-cube are located as pairs on the edge of the 5-cube. Vertices of the bitruncated 5-cube are located...	Bitruncated 5-cube

In six-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 5-orthoplex is a convex uniform 5-polytope, being a truncation

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 :...

of the regular 5-orthoplex.

There are 4 unique truncations of the 5-orthoplex. Vertices of the truncation 5-orthoplex are located as pairs on the edge of the 5-orthoplex. Vertices of the bitruncated 5-orthoplex are located on the triangular faces of the 5-orthoplex. The third and fourth truncations are more easily constructed as second and first truncations of the 5-cube.

Truncated 5-orthoplex
Type	uniform polyteron Uniform polyteron In geometry, a uniform polyteron is a five-dimensional uniform polytope. By definition, a uniform polyteron is vertex-transitive and constructed from uniform polychoron facets....
Schläfli symbol	t_0,1{3,3,3,4} t_0,1{3,3^1,1}
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... s
4-faces	42
Cells	240
Faces	400
Edges	280
Vertices	80
Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...	Elongated octahedral pyramid
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... s	BC₅, [3,3,3,4] D₅, [3^2,1,1]
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...

Alternate names

Truncated pentacross
Truncated triacontiditeron (Acronym: tot) (Jonathan Bowers)

Coordinates

Cartesian coordinates for the vertices of a truncated 5-orthoplex, centered at the origin, are all 80 vertices are sign (4) and coordinate (20) permutation

Permutation

In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...

s of

(±2,±1,0,0,0)

Images

The trunacted 5-orthoplex is constructed by a truncation

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 :...

operation applied to the 5-orthoplex. All edges are shortened, and two new vertices are added on each original edge.

Bitruncated 5-orthoplex

Bitruncated 5-orthoplex
Type	uniform polyteron Uniform polyteron In geometry, a uniform polyteron is a five-dimensional uniform polytope. By definition, a uniform polyteron is vertex-transitive and constructed from uniform polychoron facets....
Schläfli symbol	t_1,2{3,3,3,4} t_1,2{3,3^1,1}
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... s
4-faces	42
Cells	280
Faces	720
Edges	800
Vertices	320
Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...
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... s	BC₅, [3,3,3,4] D₅, [3^2,1,1]
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...

Alternate names

Bitruncated pentacross
Bitruncated triacontiditeron (Acronym: gart) (Jonathan Bowers)

Coordinates

Cartesian coordinates for the vertices of a truncated 5-orthoplex, centered at the origin, are all 80 vertices are sign and coordinate permutation

Permutation

s of

(±2,±2,±1,0,0)

Images

The bitrunacted 5-orthoplex is constructed by a bitruncation

Bitruncation

In geometry, a bitruncation is an operation on regular polytopes. It represents a truncation beyond rectification. The original edges are lost completely and the original faces remain as smaller copies of themselves....

operation applied to the 5-orthoplex. All edges are shortened, and two new vertices are added on each original edge.

Related polytopes

This polytope is one of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.

External links

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