Sphone (EntityTopic, 11)
From Hi.gher. Space
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| name=Sphone | | name=Sphone | ||
| dim=4 | | dim=4 | ||
- | | elements=1 sperical nap, 1 [[sphere]], 1 sphere surface, 0, 1 | + | | elements=1 sperical nap, 1 [[sphere]], 1 sphere surface, 0, 1 [[point]] |
| genus=0 | | genus=0 | ||
| ssc=(xyz)P | | ssc=(xyz)P |
Latest revision as of 16:28, 26 March 2017
A sphone is a special case of a pyramid where the base is a sphere. It contains the base sphere and a 3-D surface.
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 = 0
total surface area = 4π · r2
surcell volume = 4π∕3 · r2 · (r+√(r2+h2)
bulk = π∕3 · r3h
- The realmic cross-sections (n) of a sphone are:
[!x,!y,!z] ⇒ cone
[!w] ⇒ sphere of radius (r − nr∕h)
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 |
16. 1111 Tesseract | 17. 31 Sphone | 18. [21]1 Cylindrone |
List of tapertopes |