Sphone (EntityTopic, 11)
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| name=Sphone | | name=Sphone | ||
| dim=4 | | dim=4 | ||
- | | elements= | + | | elements=1 sperical nap, 1 [[sphere]], 1 sphere surface, 0, 1 [[point]] |
| genus=0 | | genus=0 | ||
| ssc=(xyz)P | | ssc=(xyz)P | ||
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}}}} | }}}} | ||
- | A '''sphone''' is a special case of a [[pyramid]] where the base is a [[sphere]]. | + | A '''sphone''' is a special case of a [[pyramid]] where the base is a [[sphere]]. It contains the base sphere and a 3-D surface. |
== Equations == | == Equations == | ||
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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 = 0<br> | <blockquote>total edge length = 0<br> | ||
- | total surface area = '' | + | total surface area = 4π · ''r''<sup>2</sup><br> |
- | surcell volume = '' | + | surcell volume = {{Over|4π|3}} · ''r''<sup>2</sup> · (''r''+√(''r''<sup>2</sup>+''h''<sup>2</sup>)<br> |
bulk = {{Over|π|3}} · ''r''<sup>3</sup>''h''</blockquote> | 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,! | + | <blockquote>[!x,!y,!z] ⇒ cone<br> |
- | [! | + | [!w] ⇒ 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}} |
Latest revision as of 16:28, 26 March 2017
A sphone is a special case of a pyramid where the base is a sphere. It contains the base sphere and a 3-D surface.
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 = 4π · r2
surcell volume = 4π∕3 · r2 · (r+√(r2+h2)
bulk = π∕3 · r3h
- The realmic cross-sections (n) of a sphone are:
[!x,!y,!z] ⇒ cone
[!w] ⇒ 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 |