Pyroteron (EntityTopic, 17)
From Hi.gher. Space
The pyroteron, also known as the hexateron, is the five-dimensional simplex. It is a special case of the pyramid where the base is a pentachoron.
Equations
- Variables:
l ⇒ length of the edges of the hexateron
- All points (x, y, z, w, φ) that lie on the surface of a hexateron will satisfy the following equation:
Unknown
- The hypervolumes of a hexateron are given by:
Unknown
- The flunic cross-sections (n) of a hexateron are:
Unknown
Incidence matrix
Dual: Self-dual
# | TXID | Va | Ea | 3a | C1a | H4.1a | Type | Name |
---|---|---|---|---|---|---|---|---|
0 | Va | = point | ; | |||||
1 | Ea | 2 | = digon | ; | ||||
2 | 3a | 3 | 3 | = triangle | ; | |||
3 | C1a | 4 | 6 | 4 | = tetrahedron | ; | ||
4 | H4.1a | 5 | 10 | 10 | 5 | = base of pyramid: pyrochoron | ; | |
5 | H5.1a | 6 | 15 | 20 | 15 | 6 | = pyroteron | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
Simplices |
triangle • tetrahedron • pyrochoron • pyroteron • pyropeton |
Notable Pentashapes | |
Flat: | pyroteron • aeroteron • geoteron |
Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
69. [11^{1}]^{2} Triangular prismic dipyramid | 70. 1^{4} Hexateron | 71. 2^{1}1^{1} Contrianglinder |
List of tapertopes |