Ditorus (EntityTopic, 11)

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Revision as of 15:02, 17 June 2007

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Geometry

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

Equations

• Variables:

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

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

(sqrt((sqrt(x² + y²) - a)² + z²) - r)² + w² = R²

• 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 ditorus are given by:

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

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

Unknown

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