Dicone (EntityTopic, 11)

From Hi.gher. Space

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<[#ontology [kind topic] [cats 4D Curved Tapertope]]>
{{STS Shape
{{STS Shape
| name=Dicone
| name=Dicone
| dim=4
| dim=4
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| elements=3, 4, 2, 2
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| elements=3, 3, 2, 2
| genus=0
| genus=0
| ssc=(xy)PP
| ssc=(xy)PP
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| extra={{STS Rotope
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| ssc2=&&T2
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| attrib=pure
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| extra={{STS Tapertope
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| notation=2<sup>2</sup> (xy)<sup>zw</sup>
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| order=1, 2
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| index=38
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| notation=2<sup>2</sup>
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| index=22
}}}}
}}}}
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A '''dicone''' is a special case of a [[pyramid]] where the base is a [[cone]]. It is also a special case of a [[dipyramid]] where the base is a [[circle]].
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A '''dicone''' is a special case of a [[pyramid]] where the base is a [[cone]]. It is also a special case of a [[dipyramid]] where the base is a [[circle]]. It is bounded by two cones and an [[arrinder]]. Its faces are a circle and two curved-cone-surfaces.
== Equations ==
== Equations ==
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''h'' ⇒ height of dicone</blockquote>
''h'' ⇒ height of dicone</blockquote>
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*All points (''x'', ''y'', ''z'', ''w'') that lie on the surface of a dicone will satisfy the following equations:
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*The [[hypervolume]]s of a dicone are given by: <span style='color: red;'>(the red equations are thought to be inaccurate and need revising!)</span>
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<blockquote>''Unknown''</blockquote>
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<blockquote><span style='color: red;'>total edge length = 2π''r'' + ''h''<br />
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total surface area = π''r''(''r'' + 2√(''r''<sup>2</sup> + ''h''<sup>2</sup>))<br />
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surcell volume = {{Over|π''rh''|3}} &middot; (2''r'' + √(''r''<sup>2</sup> + ''h''<sup>2</sup>))</span><br />
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bulk = {{Over|π|12}} &middot; ''r''<sup>2</sup>''h''<sup>2</sup></blockquote>
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*The [[hypervolume]]s of a dicone are given by:
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*The [[realmic]] [[cross-section]]s (''n'') of a dicone are:
<blockquote>''Unknown''</blockquote>
<blockquote>''Unknown''</blockquote>
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*The [[realmic]] [[cross-section]]s (''n'') of a dicone are:
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== Cross-sections ==
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<blockquote>''Unknown''</blockquote>
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Disk-first:
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<[#embed [hash QVCBEZBV33HTT7ST4B6DJE0CC0]]>
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Edge-first:
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<[#embed [hash SCYDWNKQJFQ8GJGE4JFGW8EKQD]]>
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Cone-first:
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<[#embed [hash 7Z0WP548YGM1PMNAXA7YYXCSF5]]>
== Projection ==
== Projection ==
The following are the two possible types of parallel projections for a dicone:
The following are the two possible types of parallel projections for a dicone:
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<blockquote>http://fusion-global.org/share/dicone.png</blockquote>
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<blockquote><[#embed [hash HGY0GNY4VCYQTYW4SZVVMVD0V0]]></blockquote>
The nappe-first parallel projection of the dicone into 3-space is a tetrahedron.
The nappe-first parallel projection of the dicone into 3-space is a tetrahedron.
{{Tetrashapes}}
{{Tetrashapes}}
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{{Rotope Nav|37|38|39|(II)'I<br>Coninder|<nowiki>(II)''</nowiki><br>Dicone|((II)'I)<br>Conic torus|chora}}
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{{Tapertope Nav|21|22|23|111<sup>1</sup><br>Triangular diprism|2<sup>2</sup><br>Dicone|[11]<sup>2</sup><br>Square dipyramid|chora}}

Latest revision as of 18:19, 24 April 2018


A dicone is a special case of a pyramid where the base is a cone. It is also a special case of a dipyramid where the base is a circle. It is bounded by two cones and an arrinder. Its faces are a circle and two curved-cone-surfaces.

Equations

  • Variables:
r ⇒ radius of base of dicone
h ⇒ height of dicone
  • The hypervolumes of a dicone are given by: (the red equations are thought to be inaccurate and need revising!)
total edge length = 2πr + h
total surface area = πr(r + 2√(r2 + h2))
surcell volume = πrh3 · (2r + √(r2 + h2))

bulk = π12 · r2h2
Unknown

Cross-sections

Disk-first: (image) Edge-first: (image) Cone-first: (image)

Projection

The following are the two possible types of parallel projections for a dicone:

(image)

The nappe-first parallel projection of the dicone into 3-space is a tetrahedron.


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


21. 1111
Triangular diprism
22. 22
Dicone
23. [11]2
Square dipyramid
List of tapertopes