Sphone (EntityTopic, 11)
From Hi.gher. Space
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*The [[realmic]] [[cross-section]]s (''n'') of a sphone are: | *The [[realmic]] [[cross-section]]s (''n'') of a sphone are: | ||
| - | <blockquote>[!x,!y,!w] ⇒ '' | + | <blockquote>[!x,!y,!w] ⇒ ''Hyperboloids of two sheets''<br> |
[!z] ⇒ sphere of radius (''r''-''rnh''<sup>-1</sup>)</blockquote> | [!z] ⇒ sphere of radius (''r''-''rnh''<sup>-1</sup>)</blockquote> | ||
<br clear="all"><br> | <br clear="all"><br> | ||
{{Tetrashapes}} | {{Tetrashapes}} | ||
{{Rotope Nav|20|21|22|(III)I<br>Spherinder|(III)'<br>Sphone|((III)I)<br>Toraspherinder|chora}} | {{Rotope Nav|20|21|22|(III)I<br>Spherinder|(III)'<br>Sphone|((III)I)<br>Toraspherinder|chora}} | ||
Revision as of 18:04, 10 October 2007
Template:Shape A sphone is a special case of a pyramid where the base is a sphere.
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 = Unknown
total surface area = Unknown
surcell volume = Unknown
bulk = πr3h3-1
- The realmic cross-sections (n) of a sphone are:
[!x,!y,!w] ⇒ Hyperboloids of two sheets
[!z] ⇒ sphere of radius (r-rnh-1)
| 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 |
