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
total edge length = 192l
total surface area = 240l2
total surcell volume = 160l3
surteron bulk = 60l4
surpeton pentavolume = 12l5
hexavolume = l6
[!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
pointdigonsquarecubegeochorongeoterongeopeton


Notable Hexashapes
  pyropetonaeropetongeopetonsquare 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