Runcinated 5-orthoplexes


5-orthoplex

Runcinated 5-orthoplex

Runcinated 5-cube

Runcitruncated 5-orthoplex

Runcicantellated 5-orthoplex

Runcicantitruncated 5-orthoplex

Runcitruncated 5-cube

Runcicantellated 5-cube

Runcicantitruncated 5-cube
Orthogonal projections in B5 Coxeter plane

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

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

Runcinated 5-orthoplex

Runcinated 5-orthoplex
Type Uniform 5-polytope
Schläfli symbol t0,3{3,3,3,4}
Coxeter-Dynkin diagram
4-faces 162
Cells 1200
Faces 2160
Edges 1440
Vertices 320
Vertex figure
Coxeter group B5 [4,3,3,3]
D5 [32,1,1]
Properties convex

Alternate names

Coordinates

The vertices of the can be made in 5-space, as permutations and sign combinations of:

(0,1,1,1,2)

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]

Runcitruncated 5-orthoplex

Runcitruncated 5-orthoplex
Typeuniform 5-polytope
Schläfli symbol t0,1,3{3,3,3,4}
t0,1,3{3,31,1}
Coxeter-Dynkin diagrams
4-faces162
Cells1440
Faces3680
Edges3360
Vertices960
Vertex figure
Coxeter groupsB5, [3,3,3,4]
D5, [32,1,1]
Propertiesconvex

Alternate names

Coordinates

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

(±3,±2,±1,±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]

Runcicantellated 5-orthoplex

Runcicantellated 5-orthoplex
Type Uniform 5-polytope
Schläfli symbol t0,2,3{3,3,3,4}
t0,2,3{3,3,31,1}
Coxeter-Dynkin diagram
4-faces162
Cells1200
Faces2960
Edges2880
Vertices960
Vertex figure
Coxeter group B5 [4,3,3,3]
D5 [32,1,1]
Properties convex

Alternate names

Coordinates

The vertices of the runcicantellated 5-orthoplex can be made in 5-space, as permutations and sign combinations of:

(0,1,2,2,3)

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-orthoplex

Runcicantitruncated 5-orthoplex
Type Uniform 5-polytope
Schläfli symbol t0,1,2,3{3,3,3,4}
Coxeter-Dynkin
diagram

4-faces162
Cells1440
Faces4160
Edges4800
Vertices1920
Vertex figure
Irregular 5-cell
Coxeter groups B5 [4,3,3,3]
D5 [32,1,1]
Properties convex, isogonal

Alternate names

Coordinates

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

\left(0, 1, 2, 3, 4\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]

Snub 5-demicube

The snub 5-demicube defined as an alternation of the omnitruncated 5-demicube is not uniform, but it can be given Coxeter diagram or and symmetry [32,1,1]+ or [4,(3,3,3)+], and constructed from 32 snub 5-cells, 80 alternated 6-6 duoprisms, 40 icosahedral prisms, 10 snub 24-cells, and 960 irregular tetrahedrons filling the gaps at the deleted vertices.

Related polytopes

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

Notes

  1. Klitzing, (x3o3o3x4o - spat)
  2. Klitzing, (x3x3o3x4o - pattit)
  3. Klitzing, (x3o3x3x4o - pirt)
  4. Klitzing, (x3x3x3x4o - gippit)

References

External links

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