Tesserinder (EntityTopic, 13)

From Hi.gher. Space

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Geometry

A tesserinder is a special case of the prism where the base is a cubinder.

Equations

• Variables:

r ⇒ radius of the tesserinder
a ⇒ height of the tesserinder along z-axis
b ⇒ tridth of the tesserinder along w-axis
c ⇒ pentalength of the tesserinder along φ-axis

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

x² + y² = r²
abs(z) ≤ a
abs(w) ≤ b
abs(φ) ≤ c
   -- or --
x² + y² < r²
abs(z) = a
abs(w) = b
abs(φ) = c

• The hypervolumes of a tesserinder are given by:

total edge length = Unknown
total surface area = Unknown
surcell volume = Unknown
surteron bulk = Unknown
pentavolume = πr²abc

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

Unknown

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