Tiger (EntityTopic, 11)
From Hi.gher. Space
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| - | | extra={{STS | + | | extra={{STS Toratope |
| - | | | + | | holeseq=[3] |
| - | | notation= | + | | notation=((II)(II)) |
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<blockquote>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. </blockquote> | <blockquote>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. </blockquote> | ||
{{Tetrashapes}} | {{Tetrashapes}} | ||
| - | {{ | + | {{Toratope Nav B|5|6|7|(II)II<br>Cubinder|((II)II)<br>Toracubinder|(II)(II)<br>Duocylinder|((II)(II))<br>Tiger|(III)I<br>Spherinder|((III)I)<br>Toraspherinder|chora}} |
Revision as of 20:43, 24 November 2009
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:
(sqrt(x2+y2) - a)2 + (sqrt(z2+w2) - b)2 = r2
- The parametric equations are:
x = acos(θ1) + rcos(θ1)cos(θ3)
y = asin(θ1) + rsin(θ1)cos(θ3)
z = bcos(θ2) + rcos(θ2)sin(θ3)
w = bsin(θ2) + rsin(θ2)sin(θ3)
- 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 | |||||
