# Ditorus (EntityTopic, 11)

(Redirected from Toratope 8b)

The ditorus is a four-dimensional torus formed by taking an uncapped torinder and connecting its ends either in a loop or through its inside. Its toratopic dual is itself.

## Equations

• Variables:
R ⇒ major-major radius of the ditorus
r ⇒ major-minor radius of the ditorus
ρ ⇒ minor-minor radius of the ditorus
• All points (x, y, z, w) that lie on the surcell of a ditorus will satisfy the following equation:
(√((√(x2 + y2) − ρ)2 + z2) − r)2 + w2 = R2
• The parametric equations are:
x = (R + (r + ρ cos θ3) cos θ2) cos θ1
y = (R + (r + ρ cos θ3) cos θ2) sin θ1
z = (r + ρ cos θ3) sin θ2
w = a sin θ3
total surface area = 0
surcell volume = 8π3Rrρ
bulk = 4π3ρ2rR
Unknown

## Cross-sections

Jonathan Bowers aka Polyhedron Dude created these two excellent cross-section renderings:

 Notable Tetrashapes Regular: pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron Powertopes: triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate Circular: glome • cubinder • duocylinder • spherinder • sphone • dicone • coninder Torii: tiger • toraspherinder • toracubinder • torinder • ditorus