Geoteron (EntityTopic, 20)

From Hi.gher. Space

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Geometry

A pentacube, also known as a regular decateron is a special case of the prism where the base is a tesseract.

Equations

• Variables:

l ⇒ length of the edges of the pentacube

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

Unknown

• The hypervolumes of a pentacube are given by:

total edge length = 80l
total surface area = 80l²
total surcell volume = 40l³
surteron bulk = 10l⁴
pentavolume = l⁵

• The flunic cross-sections (n) of a pentacube are:

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

Net

The net of a pentacube is a tesseract surrounded by eight more tesseracts, with one more tesseract added to one of these.

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