Sphone (EntityTopic, 11)
From Hi.gher. Space
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| - | {{Shape|Sphone|''No image''|4|2, 1, ?, 1|0|N/A|N/A|[[Line (object)|E]][[Circle|L]][[Sphere|L]]T|3<sup>1</sup>|[[Sphere]], radius 1|N/A|N/A|21}} | + | {{Shape|Sphone|''No image''|4|2, 1, ?, 1|0|N/A|N/A|[[Line (object)|E]][[Circle|L]][[Sphere|L]]T|3<sup>1</sup> xyz<sup>w</sup>|[[Sphere]], radius 1|N/A|N/A|21}} |
== Geometry == | == Geometry == | ||
| - | A '''sphone''' is a special case of a [[ | + | A '''sphone''' is a special case of a [[pyramid]] where the base is a [[sphere]]. |
=== Equations === | === Equations === | ||
| Line 14: | Line 14: | ||
*All points (''x'', ''y'', ''z'') that lie on the faces of a sphone will satisfy the following equations: | *All points (''x'', ''y'', ''z'') that lie on the faces of a sphone will satisfy the following equations: | ||
<blockquote>''x''<sup>2</sup> + ''y''<sup>2</sup> + ''z''<sup>2</sup> = ''r''<sup>2</sup><br> | <blockquote>''x''<sup>2</sup> + ''y''<sup>2</sup> + ''z''<sup>2</sup> = ''r''<sup>2</sup><br> | ||
| - | '' | + | ''w'' = 0</blockquote> |
*The [[hypervolume]]s of a sphone are given by: | *The [[hypervolume]]s of a sphone are given by: | ||
Revision as of 14:17, 17 June 2007
Geometry
A sphone is a special case of a pyramid 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
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 planar cross-sections (n) of a sphone are:
[!x,!y,!w] ⇒ Unknown
[!z] ⇒ sphere of radius (r-rnh-1)
