Aeroteron (EntityTopic, 14)
From Higher Dimensions Database
The aeroteron, also known as the icosidodecateron, the triacontaditeron and the pentacross, is the five-dimensional cross polytope, and is the dual of the geoteron.
Equations
- Variables:
l ⇒ length of the edges of the icosidodecateron
- All points (x, y, z, w, φ) that lie on the surteron of a pentacube will satisfy the following equation:
Unknown
- The hypervolumes of an icosidodecateron are given by:
Unknown
- The flunic cross-sections (n) of a n icosidodecateron are:
Unknown
Incidence matrix
Dual: geoteron
# | 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 | = pyrochoron | ; | |
5 | H5.1a | 10 | 40 | 80 | 80 | 32 | = aeroteron | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
Cross polytopes |
diamond • octahedron • aerochoron • aeroteron • aeropeton |
Notable Pentashapes | |
Flat: | pyroteron • aeroteron • geoteron |
Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
31. [IIIII] Geoteron | 32. <IIIII> Aeroteron | 33. (IIIII) Pentasphere |
List of bracketopes |