Sphone (EntityTopic, 11)

From Hi.gher. Space

Revision as of 10:57, 16 June 2007

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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)

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