Sphone (EntityTopic, 11)
From Hi.gher. Space
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:
x^{2} + y^{2} + z^{2} = r^{2}
w = 0
- The hypervolumes of a sphone are given by:
total edge length = 0
total surface area = 4π · r^{2}
surcell volume = ^{4π}∕_{3} · r^{2} · (r+√(r^{2}+h^{2})
bulk = ^{π}∕_{3} · r^{3}h
- 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 • dicone • coninder |
Torii: | tiger • torisphere • spheritorus • torinder • ditorus |
16. 1111 Tesseract | 17. 3^{1} Sphone | 18. [21]^{1} Cylindrone |
List of tapertopes |