Sphone (EntityTopic, 11)
From Hi.gher. Space
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- | {{Shape|Sphone| | + | <[#ontology [kind topic] [cats 4D Curved Tapertope]]> |
- | + | {{STS Shape | |
- | + | | attrib=pure | |
+ | | name=Sphone | ||
+ | | dim=4 | ||
+ | | elements=2, 1, 0, 1 | ||
+ | | genus=0 | ||
+ | | ssc=(xyz)P | ||
+ | | ssc2=&T3 | ||
+ | | extra={{STS Tapertope | ||
+ | | order=1, 1 | ||
+ | | notation=3<sup>1</sup> | ||
+ | | index=17 | ||
+ | }}}} | ||
- | + | A '''sphone''' is a special case of a [[pyramid]] where the base is a [[sphere]]. | |
- | + | ||
+ | == Equations == | ||
*Variables: | *Variables: | ||
<blockquote>''r'' ⇒ radius of base of sphone<br> | <blockquote>''r'' ⇒ radius of base of sphone<br> | ||
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*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: | ||
- | <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 [[ | + | *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'' | + | [!z] ⇒ sphere of radius (''r'' − {{Over|''nr''|''h''}})</blockquote> |
<br clear="all"><br> | <br clear="all"><br> | ||
- | {{ | + | {{Tetrashapes}} |
- | {{ | + | {{Tapertope Nav|16|17|18|1111<br>Tesseract|3<sup>1</sup><br>Sphone|[21]<sup>1</sup><br>Cylindrone|chora}} |
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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 |