Tiger (EntityTopic, 11)

From Hi.gher. Space

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m (Equations: add whitespace to prevent misinterpretation of a*sin x as arcsin x.)
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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
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)
total edge length = Unknown
total surface area = Unknown
surcell volume = Unknown
bulk = Unknown
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: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus


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