Sphone (EntityTopic, 11)

From Hi.gher. Space

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{{Shape|Sphone|''No image''|4|2, 1, ?, 1|0|N/A|N/A|[[Line (object)|E]][[Circle|L]][[Sphere|L]]T|3<sup>1</sup> (xyz)<sup>w</sup>|[[Sphere]], radius 1|N/A|N/A|21|N/A|N/A|pure}}
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<[#ontology [kind topic] [cats 4D Curved Tapertope]]>
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== Geometry ==
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{{STS Shape
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A '''sphone''' is a special case of a [[pyramid]] where the base is a [[sphere]].
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| attrib=pure
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| name=Sphone
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| dim=4
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| elements=1 sperical nap, 1 [[sphere]], 1 sphere surface, 0, 1 [[point]]
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| genus=0
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| ssc=(xyz)P
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| ssc2=&T3
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| extra={{STS Tapertope
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| order=1, 1
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| notation=3<sup>1</sup>
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| index=17
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}}}}
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=== Equations ===
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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.
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*Assumption: Sphone's base is centered at the origin.
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== Equations ==
*Variables:
*Variables:
<blockquote>''r'' ⇒ radius of base of sphone<br>
<blockquote>''r'' ⇒ radius of base of sphone<br>
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*The [[hypervolume]]s of a sphone are given by:
*The [[hypervolume]]s of a sphone are given by:
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<blockquote>total edge length = ''Unknown''<br>
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<blockquote>total edge length = 0<br>
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total surface area = ''Unknown''<br>
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total surface area = 4π &middot; ''r''<sup>2</sup><br>
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surcell volume = ''Unknown''<br>
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surcell volume = {{Over|4π|3}} &middot; ''r''<sup>2</sup> &middot; (''r''+√(''r''<sup>2</sup>+''h''<sup>2</sup>)<br>
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bulk = π''r''<sup>3</sup>''h''3<sup>-1</sup></blockquote>
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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:
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<blockquote>[!x,!y,!w] ⇒ ''Unknown''<br>
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<blockquote>[!x,!y,!z] ⇒ cone<br>
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[!z] ⇒ sphere of radius (''r''-''rnh''<sup>-1</sup>)</blockquote>
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[!w] ⇒ sphere of radius (''r'' − {{Over|''nr''|''h''}})</blockquote>
<br clear="all"><br>
<br clear="all"><br>
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{{Polychora}}
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{{Tetrashapes}}
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{{Rotope Nav|20|21|22|(III)I<br>Spherinder|(III)'<br>Sphone|((III)I)<br>Toraspherinder}}
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{{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
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