Ditorus (EntityTopic, 11)

(Difference between revisions)

Revision as of 10:28, 12 March 2011

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

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

total surface area = 0
surcell volume = 8π³Rrρ
bulk = 4π³ρ²rR

Unknown

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

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

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 *The parametric equations are:
 <blockquote>
-x = (R + (r + a cos th<sub>3</sub>) cos th<sub>2</sub>) cos th<sub>1</sub> <br>
+x = (R + (r + ρ cos th<sub>3</sub>) cos th<sub>2</sub>) cos th<sub>1</sub> <br>
-y = (R + (r + a cos th<sub>3</sub>) cos th<sub>2</sub>) sin th<sub>1</sub><br>
+y = (R + (r + ρ cos th<sub>3</sub>) cos th<sub>2</sub>) sin th<sub>1</sub><br>
-z = (r + a cos th<sub>3</sub>) sin th<sub>2</sub> <br>
+z = (r + ρ cos th<sub>3</sub>) sin th<sub>2</sub> <br>
 w = a sin th<sub>3</sub> </blockquote>
 *The [[hypervolume]]s of a ditorus are given by:
 <blockquote>total surface area = 0<br>
-surcell volume = 8π<sup>3</sup>Rra<br>
+surcell volume = 8π<sup>3</sup>Rrρ<br>
-bulk = 4π<sup>3</sup>a<sup>2</sup>rR</blockquote>
+bulk = 4π<sup>3</sup>ρ<sup>2</sup>rR</blockquote>
 *The [[realmic]] [[cross-section]]s (''n'') of a ditorus are: