Tesserinder (EntityTopic, 13)

From Hi.gher. Space

Latest revision as of 22:59, 11 February 2014

A tesserinder is a special case of the prism where the base is a cubinder. It is also the Cartesian product of a circle and a cube.

Its tera are six cubinders and one curved teron formed by bending an elongated tesseract into a loop in 5D. Its cells are twelve cylinders and six curved cells formed by bending elongated cubes into loops in 4D. Its faces are eight discs and twelve curved surfaces from the cylinders. Its edges are eight circles.

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