Dicone (EntityTopic, 11)
From Hi.gher. Space
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''h'' ⇒ height of dicone</blockquote> | ''h'' ⇒ height of dicone</blockquote> | ||
| - | *The [[hypervolume]]s of a dicone are given by: | + | *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> |
| - | <blockquote>total edge length = 2π''r'' + ''h''<br /> | + | <blockquote><span style='color: red;'>total edge length = 2π''r'' + ''h''<br /> |
total surface area = π''r''(''r'' + 2√(''r''<sup>2</sup> + ''h''<sup>2</sup>))<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 /> | + | surcell volume = {{Over|π''rh''|3}} · (2''r'' + √(''r''<sup>2</sup> + ''h''<sup>2</sup>))</span><br /> |
bulk = {{Over|π|12}} · ''r''<sup>2</sup>''h''<sup>2</sup></blockquote> | bulk = {{Over|π|12}} · ''r''<sup>2</sup>''h''<sup>2</sup></blockquote> | ||
Revision as of 01:54, 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: (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 = 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ExPar: [#img] is obsolete, use [#embed] instead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 | ||
