Sphone (EntityTopic, 11)

(Difference between revisions)

Revision as of 15:19, 18 November 2011

A sphone is a special case of a pyramid where the base is a sphere.

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 = Unknown
surcell volume = Unknown
bulk = ^π∕₃ · r³h

[!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

@@ Line 1: / Line 1: @@
-{{Shape
+<[#ontology [kind topic] [cats 4D Curved Tapertope]]>
+{{STS Shape
 | attrib=pure
 | name=Sphone
 | dim=4
-| elements=2, 1, ?, 1
+| elements=2, 1, 0, 1
 | genus=0
-| 20=SSC
+| ssc=(xyz)P
-| ssc=
+| ssc2=&T3
-| rns=3<sup>1</sup> (xyz)<sup>w</sup>
+| extra={{STS Tapertope
-| rot_i=21
+| order=1, 1
-| vfigure=[[Sphere]], radius 1
+| notation=3<sup>1</sup>
-}}
+| index=17
+}}}}
 A '''sphone''' is a special case of a [[pyramid]] where the base is a [[sphere]].
@@ Line 27: / Line 29: @@
 *The [[hypervolume]]s of a sphone are given by:
-<blockquote>total edge length = ''Unknown''<br>
+<blockquote>total edge length = 0<br>
 total surface area = ''Unknown''<br>
 surcell volume = ''Unknown''<br>
-bulk = π''r''<sup>3</sup>''h''3<sup>-1</sup></blockquote>
+bulk = {{Over|π|3}} &middot; ''r''<sup>3</sup>''h''</blockquote>
 *The [[realmic]] [[cross-section]]s (''n'') of a sphone are:
 <blockquote>[!x,!y,!w] ⇒ ''Hyperboloids of two sheets''<br>
-[!z] ⇒ sphere of radius (''r''-''rnh''<sup>-1</sup>)</blockquote>
+[!z] ⇒ sphere of radius (''r'' − {{Over|''nr''|''h''}})</blockquote>
 <br clear="all"><br>
 {{Tetrashapes}}
-{{Rotope Nav|20|21|22|(III)I<br>Spherinder|(III)'<br>Sphone|((III)I)<br>Toraspherinder|chora}}
+{{Tapertope Nav|16|17|18|1111<br>Tesseract|3<sup>1</sup><br>Sphone|[21]<sup>1</sup><br>Cylindrone|chora}}