Related Polytopes
It is a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 23 uniform polytera (uniform 5-polytopes) that can be constructed from the D5 symmetry of the demipenteract, 8 of which are unique to this family, and 15 are shared within the penteractic family.
t0(121) |
t0,1(121) |
t0,2(121) |
t0,3(121) |
t0,1,2(121) |
t0,1,3(121) |
t0,2,3(121) |
t0,1,2,3(121) |
The 5-demicube is third in a dimensional series of semiregular polytopes. Each progressive uniform polytope is constructed vertex figure of the previous polytope. Thorold Gosset identified this series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (5-cells and 16-cells in the case of the rectified 5-cell). In Coxeter's notation the 5-demicube is given the symbol 121.
| En | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|
| Coxeter group |
E3=A2×A1 | E4=A4 | E5=D5 | E6 | E7 | E8 | E9 = = E8+ | E10 = E8++ |
| Coxeter diagram |
||||||||
| Symmetry (order) |
(12) |
(120) |
(192) |
(51,840) |
(2,903,040) |
(696,729,600) |
(∞) |
(∞) |
| Graph | ∞ | ∞ | ||||||
| Name | −121 | 021 | 121 | 221 | 321 | 421 | 521 | 621 |
| n | 4 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|
| Coxeter group |
E3=A2×A1 | E4=A4 | E5=D5 | E6 | E7 | E8 | E9 = = E8+ | E10 = E8++ |
| Coxeter diagram |
||||||||
| Symmetry (order) |
(12) |
(120) |
(192) |
] (103,680) |
(2,903,040) |
(696,729,600) |
(∞) |
(∞) |
| Graph | ∞ | ∞ | ||||||
| Name | 1-1,2 | 102 | 112 | 122 | 132 | 142 | 152 | 162 |
Read more about this topic: 5-demicube
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