Geopeton (EntityTopic, 20)

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Revision as of 22:40, 18 November 2007

Template:Shape A hexacube, also known as a regular dodecapeton is a special case of the prism where the base is a pentacube.

Equations

• Variables:

l ⇒ length of the edges of the hexacube

• All points (x, y, z, w, φ, σ) that lie on the surpeton of a hexacube will satisfy the following equation:

Unknown

• The hypervolumes of a hexacube 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 hexacube are:

[!x, !y, !z, !w, !φ, !σ] ⇒ pentacube of side (l)

Net

The net of a hexacube is a pentacube surrounded by ten more pentacubes, with one more pentacube added to one of these.

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