Tiger (EntityTopic, 11)
From Hi.gher. Space
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*The [[realmic]] [[cross-section]]s (''n'') of a coninder are: | *The [[realmic]] [[cross-section]]s (''n'') of a coninder are: | ||
<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}} |
{{Rotope Nav|43|44|45|(II)(II)<br>Duocylinder|((II)(II))<br>Tiger|IIIII<br>Pentacube|chora}} | {{Rotope Nav|43|44|45|(II)(II)<br>Duocylinder|((II)(II))<br>Tiger|IIIII<br>Pentacube|chora}} |
Revision as of 20:19, 17 August 2007
Geometry
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(x^{2}+y^{2}) - a)^{2} + (sqrt(z^{2}+w^{2}) - b)^{2} = r^{2}
- The parametric equations are:
x = acos(θ_{1}) + rcos(θ_{1})cos(θ_{3})
y = asin(θ_{1}) + rsin(θ_{1})cos(θ_{3})
z = bcos(θ_{2}) + rcos(θ_{2})sin(θ_{3})
w = bsin(θ_{2}) + rsin(θ_{2})sin(θ_{3})
- 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 coninder 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 |