Tiger (EntityTopic, 11)

From Hi.gher. Space

(Difference between revisions)
m (fix)
m (Equations)
Line 18: Line 18:
*All points (''x'', ''y'', ''z'', ''w'') that lie on the [[surcell]] of a tiger will satisfy the following equation:
*All points (''x'', ''y'', ''z'', ''w'') that lie on the [[surcell]] of a tiger will satisfy the following equation:
-
(sqrt(''x''<sup>2</sup>+''y''<sup>2</sup>) - ''a'')<sup>2</sup> + (sqrt(''z''<sup>2</sup>+''w''<sup>2</sup>) - ''b'')<sup>2</sup> = ''r''<sup>2</sup>
+
<blockquote>((''x''<sup>2</sup> + ''y''<sup>2</sup>) ''a'')<sup>2</sup> + ((''z''<sup>2</sup> + ''w''<sup>2</sup>) ''b'')<sup>2</sup> = ''r''<sup>2</sup></blockquote>
*The [[parametric equations]] are:
*The [[parametric equations]] are:

Revision as of 10:40, 12 March 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 = 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)
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