Spheritorus (EntityTopic, 11)

From Hi.gher. Space

Of all the four-dimensional torii, the toracubinder is the closest analog to the three-dimensional torus. It is formed by taking an uncapped spherinder and connecting its ends in a loop. Its toratopic dual is the toraspherinder.

Equations

• Variables:

R ⇒ major radius of the toracubinder
r ⇒ minor radius of the toracubinder
h ⇒ height of the toracubinder

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

(√(x² + y²) − R)² + z² + w² = r²

• The parametric equations are:

x = r cos a cos b cos c + R cos c
y = r cos a cos b sin c + R sin c
z = r cos a sin b
w = r sin a

• The hypervolumes of a toracubinder are given by:

total edge length = Unknown
total surface area = Unknown
surcell volume = 4π²Rr(r+h)
bulk = 2π²Rr²h

• The realmic cross-sections (n) of a toracubinder are:

Unknown