Sphone (EntityTopic, 11)

From Hi.gher. Space

(Difference between revisions)
m
Line 4: Line 4:
| name=Sphone
| name=Sphone
| dim=4
| dim=4
-
| elements=2, 1, 0, 1
+
| elements=1 sperical nap, 1 [[sphere]], 1 sphere surface, 0, 1
| genus=0
| genus=0
| ssc=(xyz)P
| ssc=(xyz)P
Line 14: Line 14:
}}}}
}}}}
-
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 ==
Line 30: Line 30:
*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 = ''Unknown''<br>
+
total surface area = 4π &middot; ''r''<sup>2</sup><br>
-
surcell volume = ''Unknown''<br>
+
surcell volume = {{Over|4π|3}} &middot; ''r''<sup>2</sup> &middot; (''r''+√(''r''<sup>2</sup>+''h''<sup>2</sup>)<br>
bulk = {{Over|π|3}} &middot; ''r''<sup>3</sup>''h''</blockquote>
bulk = {{Over|π|3}} &middot; ''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,!z] ⇒ cone<br>
-
[!z] ⇒ sphere of radius (''r'' − {{Over|''nr''|''h''}})</blockquote>
+
[!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}}

Revision as of 16:27, 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
total edge length = 0
total surface area = 4π · r2
surcell volume = 3 · r2 · (r+√(r2+h2)
bulk = π3 · r3h
[!x,!y,!z] ⇒ cone
[!w] ⇒ sphere of radius (rnrh)




Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus


16. 1111
Tesseract
17. 31
Sphone
18. [21]1
Cylindrone
List of tapertopes