Sphone (EntityTopic, 11)
From Hi.gher. Space
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| name=Sphone | | name=Sphone | ||
| dim=4 | | dim=4 | ||
| - | | elements=2, 1, | + | | elements=2, 1, 0, 1 |
| genus=0 | | genus=0 | ||
| ssc=(xyz)P | | ssc=(xyz)P | ||
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*The [[hypervolume]]s of a sphone are given by: | *The [[hypervolume]]s of a sphone are given by: | ||
| - | <blockquote>total edge length = | + | <blockquote>total edge length = 0<br> |
total surface area = ''Unknown''<br> | total surface area = ''Unknown''<br> | ||
surcell volume = ''Unknown''<br> | surcell volume = ''Unknown''<br> | ||
| - | bulk = π''r''<sup>3</sup>''h'' | + | bulk = {{Over|π|3}} · ''r''<sup>3</sup>''h''</blockquote> |
*The [[realmic]] [[cross-section]]s (''n'') of a sphone are: | *The [[realmic]] [[cross-section]]s (''n'') of a sphone are: | ||
<blockquote>[!x,!y,!w] ⇒ ''Hyperboloids of two sheets''<br> | <blockquote>[!x,!y,!w] ⇒ ''Hyperboloids of two sheets''<br> | ||
| - | [!z] ⇒ sphere of radius (''r'' | + | [!z] ⇒ sphere of radius (''r'' − {{Over|''nr''|''h''}})</blockquote> |
<br clear="all"><br> | <br clear="all"><br> | ||
{{Tetrashapes}} | {{Tetrashapes}} | ||
{{Tapertope Nav|16|17|18|1111<br>Tesseract|3<sup>1</sup><br>Sphone|[21]<sup>1</sup><br>Cylindrone|chora}} | {{Tapertope Nav|16|17|18|1111<br>Tesseract|3<sup>1</sup><br>Sphone|[21]<sup>1</sup><br>Cylindrone|chora}} | ||
Revision as of 15:19, 18 November 2011
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 = 0
total surface area = Unknown
surcell volume = Unknown
bulk = π∕3 · r3h
- The realmic cross-sections (n) of a sphone are:
[!x,!y,!w] ⇒ Hyperboloids of two sheets
[!z] ⇒ 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 • cylindrone • dicone • coninder |
| Torii: | tiger • torisphere • spheritorus • torinder • ditorus |
| 16. 1111 Tesseract | 17. 31 Sphone | 18. [21]1 Cylindrone |
| List of tapertopes | ||
