Ditorus (EntityTopic, 11)

From Hi.gher. Space

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Geometry

The tetratorus is unique as it is the only rotope in four dimensions or less that has a pocket.

Equations

• Variables:

R ⇒ major radius of the tetratorus
r ⇒ middle radius of the tetratorus
a ⇒ minor radius of the tetratorus

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

(sqrt((sqrt(x^2 + y^2) - a)^2 + z^2) - r)^2 + w^2 = R^2

• The parametric equations are:

x = (R + (r + a cos th₃) cos th₂) cos th₁
y = (R + (r + a cos th₃) cos th₂) sin th₁
z = (r + a cos th₃) sin th₂
w = a sin th₃

• The hypervolumes of a tetratorus are given by:

total surface area = 0
surcell volume = 8π³Rra
bulk = 4π³a²rR

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

Unknown

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