Dicone (EntityTopic, 11)
From Hi.gher. Space
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| name=Dicone | | name=Dicone | ||
| dim=4 | | dim=4 | ||
| - | | elements=3, | + | | elements=3, 3, 2, 2 |
| genus=0 | | genus=0 | ||
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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]]. | + | 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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<blockquote>''r'' ⇒ radius of base of dicone<br> | <blockquote>''r'' ⇒ radius of base of dicone<br> | ||
''h'' ⇒ height of dicone</blockquote> | ''h'' ⇒ height of dicone</blockquote> | ||
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*The [[hypervolume]]s of a dicone are given by: | *The [[hypervolume]]s of a dicone are given by: | ||
| - | <blockquote>'' | + | <blockquote>total edge length = 2π''r'' + ''h''<br /> |
| + | total surface area = π''r''(''r'' + 2√(''r''<sup>2</sup> + ''h''<sup>2</sup>))<br /> | ||
| + | surcell volume = {{Over|π''rh''|3}} · (2''r'' + √(''r''<sup>2</sup> + ''h''<sup>2</sup>))<br /> | ||
| + | bulk = {{Over|π|12}} · ''r''<sup>2</sup>''h''<sup>2</sup></blockquote> | ||
*The [[realmic]] [[cross-section]]s (''n'') of a dicone are: | *The [[realmic]] [[cross-section]]s (''n'') of a dicone are: | ||
Revision as of 01:24, 23 November 2011
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:
total edge length = 2πr + h
total surface area = πr(r + 2√(r2 + h2))
surcell volume = πrh∕3 · (2r + √(r2 + h2))
bulk = π∕12 · r2h2
- The realmic cross-sections (n) of a dicone are:
Unknown
Projection
The following are the two possible types of parallel projections for a dicone:
ExPar: [#img] is obsolete, use [#embed] instead
The nappe-first parallel projection of the dicone into 3-space is a tetrahedron.
| 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 |
| 21. 1111 Triangular diprism | 22. 22 Dicone | 23. [11]2 Square dipyramid |
| List of tapertopes | ||
