D7 polytope

From Wikipedia, the free encyclopedia
Orthographic projections in the D7 Coxeter plane
7-demicube t0 D7.svg
7-demicube
CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
7-cube t6 B6.svg
7-orthoplex
CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png

In 7-dimensional geometry, there are 95 uniform polytopes with D7 symmetry, 32 are unique, and 63 are shared with the B7 symmetry. There are two regular forms, the 7-orthoplex, and 7-demicube with 14 and 64 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 32 polytopes can be made in the D7, D6, D5, D4, D3, A5, A3, Coxeter planes. Ak has [k+1] symmetry, Dk has [2(k-1)] symmetry. B7 is also included although only half of its [14] symmetry exists in these polytopes.

These 32 polytopes are each shown in these 8 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
B7
[14/2]
D7
[12]
D6
[10]
D5
[8]
D4
[6]
D3
[4]
A5
[6]
A3
[4]
1 7-demicube t0 B7.svg 7-demicube t0 D7.svg 7-demicube t0 D6.svg 7-demicube t0 D5.svg 7-demicube t0 D4.svg 7-demicube t0 D3.svg 7-demicube t0 A5.svg 7-demicube t0 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
7-demicube
Demihepteract (Hesa)
2 7-demicube t01 B7.svg 7-demicube t01 D7.svg 7-demicube t01 D6.svg 7-demicube t01 D5.svg 7-demicube t01 D4.svg 7-demicube t01 D3.svg 7-demicube t01 A5.svg 7-demicube t01 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
Cantic 7-cube
Truncated demihepteract (Thesa)
3 7-demicube t02 B7.svg 7-demicube t02 D7.svg 7-demicube t02 D6.svg 7-demicube t02 D5.svg 7-demicube t02 D4.svg 7-demicube t02 D3.svg 7-demicube t02 A5.svg 7-demicube t02 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
Runcic 7-cube
Small rhombated demihepteract (Sirhesa)
4 7-demicube t03 B7.svg 7-demicube t03 D7.svg 7-demicube t03 D6.svg 7-demicube t03 D5.svg 7-demicube t03 D4.svg 7-demicube t03 D3.svg 7-demicube t03 A5.svg 7-demicube t03 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
Steric 7-cube
Small prismated demihepteract (Sphosa)
5 7-demicube t04 B7.svg 7-demicube t04 D7.svg 7-demicube t04 D6.svg 7-demicube t04 D5.svg 7-demicube t04 D4.svg 7-demicube t04 D3.svg 7-demicube t04 A5.svg 7-demicube t04 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
Pentic 7-cube
Small cellated demihepteract (Sochesa)
6 7-demicube t05 B7.svg 7-demicube t05 D7.svg 7-demicube t05 D6.svg 7-demicube t05 D5.svg 7-demicube t05 D4.svg 7-demicube t05 D3.svg 7-demicube t05 A5.svg 7-demicube t05 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
Hexic 7-cube
Small terated demihepteract (Suthesa)
7 7-demicube t012 B7.svg 7-demicube t012 D7.svg 7-demicube t012 D6.svg 7-demicube t012 D5.svg 7-demicube t012 D4.svg 7-demicube t012 D3.svg 7-demicube t012 A5.svg 7-demicube t012 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
Runcicantic 7-cube
Great rhombated demihepteract (Girhesa)
8 7-demicube t013 B7.svg 7-demicube t013 D7.svg 7-demicube t013 D6.svg 7-demicube t013 D5.svg 7-demicube t013 D4.svg 7-demicube t013 D3.svg 7-demicube t013 A5.svg 7-demicube t013 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
Stericantic 7-cube
Prismatotruncated demihepteract (Pothesa)
9 7-demicube t023 B7.svg 7-demicube t023 D7.svg 7-demicube t023 D6.svg 7-demicube t023 D5.svg 7-demicube t023 D4.svg 7-demicube t023 D3.svg 7-demicube t023 A5.svg 7-demicube t023 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
Steriruncic 7-cube
Prismatorhomated demihepteract (Prohesa)
10 7-demicube t014 B7.svg 7-demicube t014 D7.svg 7-demicube t014 D6.svg 7-demicube t014 D5.svg 7-demicube t014 D4.svg 7-demicube t014 D3.svg 7-demicube t014 A5.svg 7-demicube t014 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
Penticantic 7-cube
Cellitruncated demihepteract (Cothesa)
11 7-demicube t024 B7.svg 7-demicube t024 D7.svg 7-demicube t024 D6.svg 7-demicube t024 D5.svg 7-demicube t024 D4.svg 7-demicube t024 D3.svg 7-demicube t024 A5.svg 7-demicube t024 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
Pentiruncic 7-cube
Cellirhombated demihepteract (Crohesa)
12 7-demicube t034 B7.svg 7-demicube t034 D7.svg 7-demicube t034 D6.svg 7-demicube t034 D5.svg 7-demicube t034 D4.svg 7-demicube t034 D3.svg 7-demicube t034 A5.svg 7-demicube t034 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
Pentisteric 7-cube
Celliprismated demihepteract (Caphesa)
13 7-demicube t015 B7.svg 7-demicube t015 D7.svg 7-demicube t015 D6.svg 7-demicube t015 D5.svg 7-demicube t015 D4.svg 7-demicube t015 D3.svg 7-demicube t015 A5.svg 7-demicube t015 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
Hexicantic 7-cube
Teritruncated demihepteract (Tuthesa)
14 7-demicube t025 B7.svg 7-demicube t025 D7.svg 7-demicube t025 D6.svg 7-demicube t025 D5.svg 7-demicube t025 D4.svg 7-demicube t025 D3.svg 7-demicube t025 A5.svg 7-demicube t025 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
Hexiruncic 7-cube
Terirhombated demihepteract (Turhesa)
15 7-demicube t035 B7.svg 7-demicube t035 D7.svg 7-demicube t035 D6.svg 7-demicube t035 D5.svg 7-demicube t035 D4.svg 7-demicube t035 D3.svg 7-demicube t035 A5.svg 7-demicube t035 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
Hexisteric 7-cube
Teriprismated demihepteract (Tuphesa)
16 7-demicube t045 B7.svg 7-demicube t045 D7.svg 7-demicube t045 D6.svg 7-demicube t045 D5.svg 7-demicube t045 D4.svg 7-demicube t045 D3.svg 7-demicube t045 A5.svg 7-demicube t045 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
Hexipentic 7-cube
Tericellated demihepteract (Tuchesa)
17 7-demicube t0123 B7.svg 7-demicube t0123 D7.svg 7-demicube t0123 D6.svg 7-demicube t0123 D5.svg 7-demicube t0123 D4.svg 7-demicube t0123 D3.svg 7-demicube t0123 A5.svg 7-demicube t0123 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
Steriruncicantic 7-cube
Great prismated demihepteract (Gephosa)
18 7-demicube t0124 B7.svg 7-demicube t0124 D7.svg 7-demicube t0124 D6.svg 7-demicube t0124 D5.svg 7-demicube t0124 D4.svg 7-demicube t0124 D3.svg 7-demicube t0124 A5.svg 7-demicube t0124 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
Pentiruncicantic 7-cube
Celligreatorhombated demihepteract (Cagrohesa)
19 7-demicube t0134 B7.svg 7-demicube t0134 D7.svg 7-demicube t0134 D6.svg 7-demicube t0134 D5.svg 7-demicube t0134 D4.svg 7-demicube t0134 D3.svg 7-demicube t0134 A5.svg 7-demicube t0134 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
Pentistericantic 7-cube
Celliprismatotruncated demihepteract (Capthesa)
20 7-demicube t0234 B7.svg 7-demicube t0234 D7.svg 7-demicube t0234 D6.svg 7-demicube t0234 D5.svg 7-demicube t0234 D4.svg 7-demicube t0234 D3.svg 7-demicube t0234 A5.svg 7-demicube t0234 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
Pentisteriruncic 7-cube
Celliprismatorhombated demihepteract (Coprahesa)
21 7-demicube t0125 B7.svg 7-demicube t0125 D7.svg 7-demicube t0125 D6.svg 7-demicube t0125 D5.svg 7-demicube t0125 D4.svg 7-demicube t0125 D3.svg 7-demicube t0125 A5.svg 7-demicube t0125 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
Hexiruncicantic 7-cube
Terigreatorhombated demihepteract (Tugrohesa)
22 7-demicube t0135 B7.svg 7-demicube t0135 D7.svg 7-demicube t0135 D6.svg 7-demicube t0135 D5.svg 7-demicube t0135 D4.svg 7-demicube t0135 D3.svg 7-demicube t0135 A5.svg 7-demicube t0135 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
Hexistericantic 7-cube
Teriprismatotruncated demihepteract (Tupthesa)
23 7-demicube t0235 B7.svg 7-demicube t0235 D7.svg 7-demicube t0235 D6.svg 7-demicube t0235 D5.svg 7-demicube t0235 D4.svg 7-demicube t0235 D3.svg 7-demicube t0235 A5.svg 7-demicube t0235 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
Hexisteriruncic 7-cube
Teriprismatorhombated demihepteract (Tuprohesa)
24 7-demicube t0145 B7.svg 7-demicube t0145 D7.svg 7-demicube t0145 D6.svg 7-demicube t0145 D5.svg 7-demicube t0145 D4.svg 7-demicube t0145 D3.svg 7-demicube t0145 A5.svg 7-demicube t0145 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
Hexipenticantic 7-cube
Tericellitruncated demihepteract (Tucothesa)
25 7-demicube t0245 B7.svg 7-demicube t0245 D7.svg 7-demicube t0245 D6.svg 7-demicube t0245 D5.svg 7-demicube t0245 D4.svg 7-demicube t0245 D3.svg 7-demicube t0245 A5.svg 7-demicube t0245 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
Hexipentiruncic 7-cube
Tericellirhombated demihepteract (Tucrohesa)
26 7-demicube t0345 B7.svg 7-demicube t0345 D7.svg 7-demicube t0345 D6.svg 7-demicube t0345 D5.svg 7-demicube t0345 D4.svg 7-demicube t0345 D3.svg 7-demicube t0345 A5.svg 7-demicube t0345 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
Hexipentisteric 7-cube
Tericelliprismated demihepteract (Tucophesa)
27 7-demicube t01234 B7.svg 7-demicube t01234 D7.svg 7-demicube t01234 D6.svg 7-demicube t01234 D5.svg 7-demicube t01234 D4.svg 7-demicube t01234 D3.svg 7-demicube t01234 A5.svg 7-demicube t01234 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
Pentisteriruncicantic 7-cube
Great cellated demihepteract (Gochesa)
28 7-demicube t01235 B7.svg 7-demicube t01235 D7.svg 7-demicube t01235 D6.svg 7-demicube t01235 D5.svg 7-demicube t01235 D4.svg 7-demicube t01235 D3.svg 7-demicube t01235 A5.svg 7-demicube t01235 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
Hexisteriruncicantic 7-cube
Terigreatoprimated demihepteract (Tugphesa)
29 7-demicube t01245 B7.svg 7-demicube t01245 D7.svg 7-demicube t01245 D6.svg 7-demicube t01245 D5.svg 7-demicube t01245 D4.svg 7-demicube t01245 D3.svg 7-demicube t01245 A5.svg 7-demicube t01245 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
Hexipentiruncicantic 7-cube
Tericelligreatorhombated demihepteract (Tucagrohesa)
30 7-demicube t01345 B7.svg 7-demicube t01345 D7.svg 7-demicube t01345 D6.svg 7-demicube t01345 D5.svg 7-demicube t01345 D4.svg 7-demicube t01345 D3.svg 7-demicube t01345 A5.svg 7-demicube t01345 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
Hexipentistericantic 7-cube
Tericelliprismatotruncated demihepteract (Tucpathesa)
31 7-demicube t02345 B7.svg 7-demicube t02345 D7.svg 7-demicube t02345 D6.svg 7-demicube t02345 D5.svg 7-demicube t02345 D4.svg 7-demicube t02345 D3.svg 7-demicube t02345 A5.svg 7-demicube t02345 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
Hexipentisteriruncic 7-cube
Tericellprismatorhombated demihepteract (Tucprohesa)
32 7-demicube t012345 B7.svg 7-demicube t012345 D7.svg 7-demicube t012345 D6.svg 7-demicube t012345 D5.svg 7-demicube t012345 D4.svg 7-demicube t012345 D3.svg 7-demicube t012345 A5.svg 7-demicube t012345 A3.svg CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png = CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
Hexipentisteriruncicantic 7-cube
Great terated demihepteract (Guthesa)

References

  • H.S.M. Coxeter:
    • H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
  • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
    • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
    • (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
    • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
  • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
  • Klitzing, Richard. "7D uniform polytopes (polyexa)". 

Notes

  1. ^ Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter
Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn
Regular polygon Triangle Square p-gon Hexagon Pentagon
Uniform polyhedron Tetrahedron OctahedronCube Demicube DodecahedronIcosahedron
Uniform 4-polytope 5-cell 16-cellTesseract Demitesseract 24-cell 120-cell600-cell
Uniform 5-polytope 5-simplex 5-orthoplex5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex6-cube 6-demicube 122221
Uniform 7-polytope 7-simplex 7-orthoplex7-cube 7-demicube 132231321
Uniform 8-polytope 8-simplex 8-orthoplex8-cube 8-demicube 142241421
Uniform 9-polytope 9-simplex 9-orthoplex9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplexn-cube n-demicube 1k22k1k21 n-pentagonal polytope
Topics: Polytope familiesRegular polytopeList of regular polytopes and compounds
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