Tiger (EntityTopic, 11)
From Hi.gher. Space
(Difference between revisions)
m (→Equations: add whitespace to prevent misinterpretation of a*sin x as arcsin x.) |
(add construction image) |
||
Line 11: | Line 11: | ||
| index=6b | | index=6b | ||
}}}} | }}}} | ||
+ | |||
+ | <[#img [hash MGZY4K399MQ5APN1T9QXTKFA7F] [width 900]]><br/> | ||
+ | ''Diagram created by [[Keiji]], adapted from [http://teamikaria.com/hddb/forum/download/file.php?id=63 a sketch] from [[Secret]] in [http://teamikaria.com/hddb/forum/viewtopic.php?p=19287#p19287 this forum post].'' | ||
== Equations == | == Equations == |
Revision as of 21:00, 27 November 2013
ExPar: [#img] is obsolete, use [#embed] instead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.
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 |