Ditorus (EntityTopic, 11)

From Higher Dimensions Database


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 three excellent cross-section renderings:
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Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonediconeconinder
Torii: tigertorispherespheritorustorinderditorus


7a. (III)I
Spherinder
7b. ((III)I)
Torisphere
8a. ((II)I)I
Torinder
8b. (((II)I)I)
Ditorus
9a. IIIII
Penteract
9b. (IIIII)
Pentasphere
List of toratopes