Tiger (EntityTopic, 11)
From Hi.gher. Space
ExPar: [#img] is obsolete, use [#embed] instead
Diagram created by Keiji, adapted from a sketch from Secret in this forum post.
Equations
- Variables:
a ⇒ major radius of the tiger in the xy plane
b ⇒ major radius of the tiger in the zw plane
r ⇒ minor radius of the tiger
- All points (x, y, z, w) that lie on the surcell of a tiger will satisfy the following equation:
(√(x^{2} + y^{2}) − a)^{2} + (√(z^{2} + w^{2}) − b)^{2} = r^{2}
- The parametric equations are:
x = a cos(θ_{1}) + r cos(θ_{1})cos(θ_{3})
y = a sin(θ_{1}) + r sin(θ_{1})cos(θ_{3})
z = b cos(θ_{2}) + r cos(θ_{2})sin(θ_{3})
w = b sin(θ_{2}) + r sin(θ_{2})sin(θ_{3})
- The hypervolumes of a tiger are given by:
total edge length = Unknown
total surface area = Unknown
surcell volume = Unknown
bulk = Unknown
- The realmic cross-sections (n) of a tiger are:
For realms parallel to one of the axes, they are formed by rotating Cassini ovals around a line parallel with their major axis, and not intersecting the ovals.
Cross-sections
Jonathan Bowers aka Polyhedron Dude created these two excellent cross-section renderings: ExPar: [#img] is obsolete, use [#embed] instead ExPar: [#img] is obsolete, use [#embed] instead
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 |
5a. (II)II Cubinder | 5b. ((II)II) Toracubinder | 6a. (II)(II) Duocylinder | 6b. ((II)(II)) Tiger | 7a. (III)I Spherinder | 7b. ((III)I) Toraspherinder |
List of toratopes |