Ditorus (EntityTopic, 11)
From Hi.gher. Space
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Revision as of 07:19, 20 June 2007
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
