Tiger (EntityTopic, 11)
From Hi.gher. Space
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*The [[parametric equations]] are: | *The [[parametric equations]] are: | ||
- | <blockquote>''x'' = ''a''cos(''θ<sub>1</sub>'') + ''r''cos(''θ<sub>1</sub>'')cos(''θ<sub>3</sub>'')<br> | + | <blockquote>''x'' = ''a'' cos(''θ<sub>1</sub>'') + ''r'' cos(''θ<sub>1</sub>'')cos(''θ<sub>3</sub>'')<br> |
- | ''y'' = ''a''sin(''θ<sub>1</sub>'') + ''r''sin(''θ<sub>1</sub>'')cos(''θ<sub>3</sub>'')<br> | + | ''y'' = ''a'' sin(''θ<sub>1</sub>'') + ''r'' sin(''θ<sub>1</sub>'')cos(''θ<sub>3</sub>'')<br> |
- | ''z'' = ''b''cos(''θ<sub>2</sub>'') + ''r''cos(''θ<sub>2</sub>'')sin(''θ<sub>3</sub>'')<br> | + | ''z'' = ''b'' cos(''θ<sub>2</sub>'') + ''r'' cos(''θ<sub>2</sub>'')sin(''θ<sub>3</sub>'')<br> |
- | ''w'' = ''b''sin(''θ<sub>2</sub>'') + ''r''sin(''θ<sub>2</sub>'')sin(''θ<sub>3</sub>'')</blockquote> | + | ''w'' = ''b'' sin(''θ<sub>2</sub>'') + ''r'' sin(''θ<sub>2</sub>'')sin(''θ<sub>3</sub>'')</blockquote> |
*The [[hypervolume]]s of a tiger are given by: | *The [[hypervolume]]s of a tiger are given by: |
Revision as of 23:04, 17 November 2011
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:
(√(x2 + y2) − a)2 + (√(z2 + w2) − b)2 = r2
- The parametric equations are:
x = a cos(θ1) + r cos(θ1)cos(θ3)
y = a sin(θ1) + r sin(θ1)cos(θ3)
z = b cos(θ2) + r cos(θ2)sin(θ3)
w = b sin(θ2) + r sin(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 |