Spheritorus (EntityTopic, 11)

(Redirected from Toratope 5b)

Of all the four-dimensional torii, the spheritorus, previously known as the toracubinder, is the closest analog to the three-dimensional torus. It is formed by taking an uncapped spherinder and connecting its ends in a loop. Its toratopic dual is the torisphere. It has two possible cross-sections in coordinate planes through the origin: the torus, and two disjoint spheres.

Equations

• Variables:
R ⇒ major radius of the spheritorus
r ⇒ minor radius of the spheritorus
h ⇒ height of the spheritorus
• All points (x, y, z, w) that lie on the surcell of a spheritorus will satisfy the following equation:
(√(x2 + y2) − R)2 + z2 + w2 = r2
• The parametric equations are:
x = r cos a cos b cos c + R cos c
y = r cos a cos b sin c + R sin c
z = r cos a sin b
w = r sin a
total edge length = Unknown
total surface area = Unknown
surcell volume = 4π2Rr(r+h)
bulk = 2π2Rr2h
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 • cylindrone • dicone • coninder Torii: tiger • torisphere • spheritorus • torinder • ditorus

 4a. IIIITesseract 4b. (IIII)Glome 5a. (II)IICubinder 5b. ((II)II)Spheritorus 6a. (II)(II)Duocylinder 6b. ((II)(II))Tiger List of toratopes