# D7 polytope

Orthographic projections in the D$_7$ Coxeter plane :
| 7-demicube | 7-orthoplex |
In 7-dimensional geometry, there are 95 uniform polytopes with D$_7$ symmetry; 32 are unique, and 63 are shared with the B$_7$ 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 D$_6$ Coxeter group, and other subgroups.

## Graphs

Symmetric orthographic projections of these 32 polytopes can be made in the D$_7$, D$_6$, D$_5$, D$_4$, D$_3$, A$_5$, A$_3$, Coxeter planes. A$_k$ has [k+1] symmetry, D$_k$ has [2(k-1)] symmetry. B$_7$ 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 plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter diagram Names |
| # | B$_7$ [14/2] | D$_7$ [12] | D$_6$ [10] | D$_5$ [8] | D$_4$ [6] | D$_3$ [4] | A$_5$ [6] | A$_3$ [4] | Coxeter diagram Names |
| 1 | | | | | | | | | = 7-demicube Demihepteract (Hesa) |
| 2 | | | | | | | | | = Cantic 7-cube Truncated demihepteract (Thesa) |
| 3 | | | | | | | | | = Runcic 7-cube Small rhombated demihepteract (Sirhesa) |
| 4 | | | | | | | | | = Steric 7-cube Small prismated demihepteract (Sphosa) |
| 5 | | | | | | | | | = Pentic 7-cube Small cellated demihepteract (Sochesa) |
| 6 | | | | | | | | | = Hexic 7-cube Small terated demihepteract (Suthesa) |
| 7 | | | | | | | | | = Runcicantic 7-cube Great rhombated demihepteract (Girhesa) |
| 8 | | | | | | | | | = Stericantic 7-cube Prismatotruncated demihepteract (Pothesa) |
| 9 | | | | | | | | | = Steriruncic 7-cube Prismatorhomated demihepteract (Prohesa) |
| 10 | | | | | | | | | = Penticantic 7-cube Cellitruncated demihepteract (Cothesa) |
| 11 | | | | | | | | | = Pentiruncic 7-cube Cellirhombated demihepteract (Crohesa) |
| 12 | | | | | | | | | = Pentisteric 7-cube Celliprismated demihepteract (Caphesa) |
| 13 | | | | | | | | | = Hexicantic 7-cube Teritruncated demihepteract (Tuthesa) |
| 14 | | | | | | | | | = Hexiruncic 7-cube Terirhombated demihepteract (Turhesa) |
| 15 | | | | | | | | | = Hexisteric 7-cube Teriprismated demihepteract (Tuphesa) |
| 16 | | | | | | | | | = Hexipentic 7-cube Tericellated demihepteract (Tuchesa) |
| 17 | | | | | | | | | = Steriruncicantic 7-cube Great prismated demihepteract (Gephosa) |
| 18 | | | | | | | | | = Pentiruncicantic 7-cube Celligreatorhombated demihepteract (Cagrohesa) |
| 19 | | | | | | | | | = Pentistericantic 7-cube Celliprismatotruncated demihepteract (Capthesa) |
| 20 | | | | | | | | | = Pentisteriruncic 7-cube Celliprismatorhombated demihepteract (Coprahesa) |
| 21 | | | | | | | | | = Hexiruncicantic 7-cube Terigreatorhombated demihepteract (Tugrohesa) |
| 22 | | | | | | | | | = Hexistericantic 7-cube Teriprismatotruncated demihepteract (Tupthesa) |
| 23 | | | | | | | | | = Hexisteriruncic 7-cube Teriprismatorhombated demihepteract (Tuprohesa) |
| 24 | | | | | | | | | = Hexipenticantic 7-cube Tericellitruncated demihepteract (Tucothesa) |
| 25 | | | | | | | | | = Hexipentiruncic 7-cube Tericellirhombated demihepteract (Tucrohesa) |
| 26 | | | | | | | | | = Hexipentisteric 7-cube Tericelliprismated demihepteract (Tucophesa) |
| 27 | | | | | | | | | = Pentisteriruncicantic 7-cube Great cellated demihepteract (Gochesa) |
| 28 | | | | | | | | | = Hexisteriruncicantic 7-cube Terigreatoprimated demihepteract (Tugphesa) |
| 29 | | | | | | | | | = Hexipentiruncicantic 7-cube Tericelligreatorhombated demihepteract (Tucagrohesa) |
| 30 | | | | | | | | | = Hexipentistericantic 7-cube Tericelliprismatotruncated demihepteract (Tucpathesa) |
| 31 | | | | | | | | | = Hexipentisteriruncic 7-cube Tericellprismatorhombated demihepteract (Tucprohesa) |
| 32 | | | | | | | | | = Hexipentisteriruncicantic 7-cube Great terated demihepteract (Guthesa) |