Tiger (EntityTopic, 11)

From Hi.gher. Space

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Revision as of 17:38, 19 December 2010


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

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