Geopeton (EntityTopic, 20)
From Hi.gher. Space
The geopeton, also known as the hexeract, the hexacube and the regular dodecapeton is the six-dimensional hypercube. It is a special case of the prism where the base is a geoteron. It is also the square of the cube.
Equations
- Variables:
l ⇒ length of the edges of the hexeract
- All points (x, y, z, w, φ, σ) that lie on the surpeton of a hexeract will satisfy the following equation:
Unknown
- The hypervolumes of a hexeract are given by:
total edge length = 192l
total surface area = 240l2
total surcell volume = 160l3
surteron bulk = 60l4
surpeton pentavolume = 12l5
hexavolume = l6
- The pentaplanar cross-sections (n) of a hexeract are:
[!x, !y, !z, !w, !φ, !σ] ⇒ pentacube of side (l)
Net
The net of a hexeract is a penteract surrounded by ten more penteracts, with one more penteract added to one of these.
Hypercubes |
point • digon • square • cube • geochoron • geoteron • geopeton |
Notable Hexashapes | |
pyropeton • aeropeton • geopeton • square cubic truncatriate |
83. 21111 Penterinder | 84. 111111 Hexeract | 85. 51 Pentaspheric cone |
List of tapertopes |
20a. (((II)I)I)I Ditorinder | 20b. ((((II)I)I)I) Tritorus | 21a. IIIIII Hexeract | 21b. (IIIIII) Hexasphere | 22a. (II)IIII Penterinder | 22b. ((II)III) Torapenterinder |
List of toratopes |
193. (<xy><(zw)φ>) Unknown shape | 194. [xyzwφσ] Hexeract | 195. [<xy>zwφσ] Narrow hexeract |
List of bracketopes |