List of D6 polytopes

Orthographic projections in the D6 Coxeter plane

6-demicube

6-orthoplex

In 6-dimensional geometry, there are 47 uniform polytopes with D6 symmetry, 16 are unique, and 31 are shared with the B6 symmetry. There are two regular forms, the 6-orthoplex, and 6-demicube with 12 and 32 vertices respectively.

They can be visualized as symmetric orthographic projections in Coxeter planes of the D6 Coxeter group, and other subgroups.

Graphs

Symmetric orthographic projections of these 16 polytopes can be made in the D6, D5, D4, D3, A5, A3, Coxeter planes. Ak has [k+1] symmetry, Dk has [2(k-1)] symmetry. B6 is also included although only half of its [12] symmetry exists in these polytopes.

These 16 polytopes are each shown in these 7 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.

# Coxeter plane graphs Coxeter diagram
Names
B6
[12/2]
D6
[10]
D5
[8]
D4
[6]
D3
[4]
A5
[6]
A3
[4]
1
6-demicube
Hemihexeract (hax)
2
Truncated 6-demicube
Truncated hemihexeract (thax)
3
Cantellated 6-demicube
Small rhombated hemihexeract (sirhax)
4
Runcinated 6-demicube
Small prismated hemihexeract (sophax)
5
Stericated 6-demicube
Small cellated demihexeract (sochax)
6
Cantitruncated 6-demicube
Great rhombated hemihexeract (girhax)
7
Runcitruncated 6-demicube
Prismatotruncated hemihexeract (pithax)
8
Runcicantellated 6-demicube
Prismatorhombated hemihexeract (prohax)
9
Runcitruncated 6-demicube
Cellitruncated hemihexeract (cathix)
10
Stericantellated 6-demicube
Cellirhombated hemihexeract (crohax)
11
Steriruncinated 6-demicube
Celliprismated hemihexeract (cophix)
12
Runcicantitruncated 6-demicube
Great prismated hemihexeract (gophax)
13
Stericantitruncated 6-demicube
Celligreatorhombated hemihexeract (cagrohax)
14
Steriruncitruncated 6-demicube
Celliprismatotruncated hemihexeract (capthix)
15
Steriruncicantellated 6-demicube
Celliprismatorhombated hemihexeract (caprohax)
16
Steriruncicantitruncated 6-demicube
Great cellated hemihexeract (gochax)

References

Notes

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