Runcinated 5-cubes


5-cube

Runcinated 5-cube

Runcinated 5-orthoplex

Runcitruncated 5-cube

Runcicantellated 5-cube

Runcicantitruncated 5-cube

Runcitruncated 5-orthoplex

Runcicantellated 5-orthoplex

Runcicantitruncated 5-orthoplex
Orthogonal projections in B5 Coxeter plane

In five-dimensional geometry, a runcinated 5-cube is a convex uniform 5-polytope that is a runcination (a 3rd order truncation) of the regular 5-cube.

There are unique 8 degrees of runcinations of the 5-cube, along with permutations of truncations, and cantellations. Four are more simply constructed relative to the 5-orthoplex.

Runcinated 5-cube

Runcinated 5-cube
Type Uniform 5-polytope
Schläfli symbol t0,3{4,3,3,3}
Coxeter diagram
4-faces 202
Cells 1240
Faces 2160
Edges 1440
Vertices 320
Vertex figure
3-3 duoprism
Coxeter group B5 [4,3,3,3]
Properties convex

Alternate names

Coordinates

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

\left(\pm1,\ \pm1,\ \pm1,\ \pm(1+\sqrt{2}),\ \pm(1+\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]

Runcitruncated 5-cube

Runcitruncated 5-cube
Typeuniform polyteron
Schläfli symbol t0,1,3{4,3,3,3}
Coxeter-Dynkin diagrams
4-faces202
Cells1560
Faces3760
Edges3360
Vertices960
Vertex figure
Coxeter groupsB5, [3,3,3,4]
Propertiesconvex

Alternate names

Construction and coordinates

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

\left(\pm1,\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2}),\ \pm(1+2\sqrt{2}),\ \pm(1+2\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]

Runcicantellated 5-cube

Runcicantellated 5-cube
Type Uniform 5-polytope
Schläfli symbol t0,2,3{4,3,3,3}
Coxeter-Dynkin diagram
4-faces202
Cells1240
Faces2960
Edges2880
Vertices960
Vertex figure
Coxeter group B5 [4,3,3,3]
Properties convex

Alternate names

Coordinates

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

\left(\pm1,\ \pm1,\ \pm(1+\sqrt{2}),\ \pm(1+2\sqrt{2}),\ \pm(1+2\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]

Runcicantitruncated 5-cube

Runcicantitruncated 5-cube
Type Uniform 5-polytope
Schläfli symbol t0,1,2,3{4,3,3,3}
Coxeter-Dynkin
diagram
4-faces202
Cells1560
Faces4240
Edges4800
Vertices1920
Vertex figure
Irregular 5-cell
Coxeter group B5 [4,3,3,3]
Properties convex, isogonal

Alternate names

Coordinates

The Cartesian coordinates of the vertices of a runcicantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:

\left(1,\ 1+\sqrt{2},\ 1+2\sqrt{2},\ 1+3\sqrt{2},\ 1+3\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]

Related polytopes

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

References

External links

This article is issued from Wikipedia - version of the Thursday, April 30, 2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.