Torisphere (EntityTopic, 11)

From Hi.gher. Space

Revision as of 18:19, 29 November 2009

The toraspherinder is a four-dimensional torus formed by taking an uncapped spherinder and connecting its ends through its inside. It can also be formed by taking an uncapped cubinder and connecting its ends in a loop. Its toratopic dual is therefore the toracubinder.

Equations

• Variables:

r ⇒ minor radius of the toraspherinder
R ⇒ major radius of the toraspherinder

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

(sqrt(x²+y²+z²)-R)² + w² = r²

• The parametric equations are:

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

• The hypervolumes of a toraspherinder are given by:

total edge length = 0
total surface area = 0
surcell volume = 8π²Rr²
bulk = 8π²Rr³3^-1

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

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