Cantellated 5-cube


5-cube

Cantellated 5-cube

Bicantellated 5-cube

Cantellated 5-orthoplex

5-orthoplex

Cantitruncated 5-cube

Bicantitruncated 5-cube

Cantitruncated 5-orthoplex
Orthogonal projections in BC5 Coxeter plane

In six-dimensional geometry, a cantellated 5-cube is a convex uniform 5-polytope, being a cantellation of the regular 5-cube.

There are 6 unique cantellation for the 5-cube, including truncations. Half of them are more easily constructed from the dual 5-orthoplex

Contents


Cantellated 5-cube

Cantellated 5-cube
Type Uniform 5-polytope
Schläfli symbol t0,2{4,3,3,3}
Coxeter-Dynkin diagram
4-faces 82
Cells 640
Faces 1520
Edges 1200
Vertices 240
Vertex figure
Coxeter group BC5 [4,3,3,3]
Properties convex

Alternate names

Coordinates

The Cartesian coordinates of the vertices of a cantellated 5-cube having edge length 2 are all permutations of:

\left(\pm1,\ \pm1,\ \pm(1%2B\sqrt{2}),\ \pm(1%2B\sqrt{2}),\ \pm(1%2B\sqrt{2})\right)

Images

orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph
Dihedral symmetry [4] [4]

Bicantellated 5-cube

Bicantellated 5-cube
Type Uniform 5-polytope
Schläfli symbol t1,3{4,3,3,3}
Coxeter-Dynkin diagram
4-faces 122
Cells 840
Faces 2160
Edges 1920
Vertices 480
Vertex figure
Coxeter group BC5 [4,3,3,3]
Properties convex

In five-dimensional geometry, a bicantellated 5-cube is a uniform 5-polytope.

Alternate names

Coordinates

The Cartesian coordinates of the vertices of a bicantellated 5-cube having edge length 2 are all permutations of:

(0,1,1,2,2)

Images

orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph
Dihedral symmetry [4] [4]

Cantitruncated 5-cube

Cantitruncated 5-cube
Type Uniform 5-polytope
Schläfli symbol t0,1,2{4,3,3,3}
Coxeter-Dynkin
diagram
4-faces 82
Cells 640
Faces 1520
Edges 1440
Vertices 480
Vertex figure
Coxeter group BC5 [4,3,3,3]
Properties convex, isogonal

Alternate names

Coordinates

The Cartesian coordinates of the vertices of an cantitruncated tesseract having an edge length of 2 are given by all permutations of coordinates and sign of:

\left(1,\ 1%2B\sqrt{2},\ 1%2B2\sqrt{2},\ 1%2B2\sqrt{2},\ 1%2B2\sqrt{2}\right)

Images

orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph
Dihedral symmetry [4] [4]

Bicantitruncated 5-cube

Bicantitruncated 5-cube
Type uniform polyteron
Schläfli symbol t1,2,3{3,3,3,4}
t1,2,3{3,31,1}
Coxeter-Dynkin diagrams
4-faces 122
Cells 840
Faces 2160
Edges 2400
Vertices 960
Vertex figure
Coxeter groups BC5, [3,3,3,4]
D5, [32,1,1]
Properties convex

Alternate names

Coordinates

Cartesian coordinates for the vertices of a cantitruncated 5-cube, centered at the origin, are all sign and coordinate permutations of

(±3,±3,±2,±1,0)

Images

orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph
Dihedral symmetry [4] [4]

Related polytopes

These polytopes are from a set of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.


β5

t1β5

t2γ5

t1γ5

γ5

t0,1β5

t0,2β5

t1,2β5

t0,3β5

t1,3γ5

t1,2γ5

t0,4γ5

t0,3γ5

t0,2γ5

t0,1γ5

t0,1,2β5

t0,1,3β5

t0,2,3β5

t1,2,3γ5

t0,1,4β5

t0,2,4γ5

t0,2,3γ5

t0,1,4γ5

t0,1,3γ5

t0,1,2γ5

t0,1,2,3β5

t0,1,2,4β5

t0,1,3,4γ5

t0,1,2,4γ5

t0,1,2,3γ5

t0,1,2,3,4γ5

References

External links