Sphone (EntityTopic, 11)
From Hi.gher. Space
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| - | {{Shape | + | {{STS Shape |
| attrib=pure | | attrib=pure | ||
| name=Sphone | | name=Sphone | ||
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| elements=2, 1, ?, 1 | | elements=2, 1, ?, 1 | ||
| genus=0 | | genus=0 | ||
| - | |||
| ssc=(xyz)P | | ssc=(xyz)P | ||
| - | | | + | | extra={{STS Rotope |
| - | | | + | | attrib=pure |
| + | | notation=3<sup>1</sup> (xyz)<sup>w</sup> | ||
| + | | index=21 | ||
| + | }}{{STS Uniform polytope | ||
| vfigure=[[Sphere]], radius 1 | | vfigure=[[Sphere]], radius 1 | ||
| - | }} | + | }}}} |
A '''sphone''' is a special case of a [[pyramid]] where the base is a [[sphere]]. | A '''sphone''' is a special case of a [[pyramid]] where the base is a [[sphere]]. | ||
Revision as of 15:51, 14 March 2008
A sphone is a special case of a pyramid where the base is a sphere.
Equations
- Variables:
r ⇒ radius of base of sphone
h ⇒ height of sphone
- All points (x, y, z, w) that lie on the surcell of a sphone will satisfy the following equations:
Unknown
- All points (x, y, z) that lie on the faces of a sphone will satisfy the following equations:
x2 + y2 + z2 = r2
w = 0
- The hypervolumes of a sphone are given by:
total edge length = Unknown
total surface area = Unknown
surcell volume = Unknown
bulk = πr3h3-1
- The realmic cross-sections (n) of a sphone are:
[!x,!y,!w] ⇒ Hyperboloids of two sheets
[!z] ⇒ sphere of radius (r-rnh-1)
| 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 |
