Sphone (EntityTopic, 11)
From Hi.gher. Space
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Geometry
A sphone is a special case of a tetrapyramid where the base is a sphere.
Equations
- Assumption: Sphone's base is centered at the origin.
- 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
z = 0
- The hypervolumes of a sphone are given by:
total edge length = Unknown
total surface area = Unknown
surcell volume = Unknown
bulk = πr3h3-1
- The planar cross-sections (n) of a sphone are:
[!x,!y,!w] ⇒ Unknown
[!z] ⇒ sphere of radius (r-rnh-1)
Template:Polychora
Template:Rotopes
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