Dicone (EntityTopic, 11)
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| - | {{Shape|Dicone| | + | <[#ontology [kind topic] [cats 4D Curved Tapertope]]> |
| + | {{STS Shape | ||
| + | | name=Dicone | ||
| + | | dim=4 | ||
| + | | elements=3, 3, 2, 2 | ||
| + | | genus=0 | ||
| + | | ssc=(xy)PP | ||
| + | | ssc2=&&T2 | ||
| + | | extra={{STS Tapertope | ||
| + | | order=1, 2 | ||
| + | | notation=2<sup>2</sup> | ||
| + | | index=22 | ||
| + | }}}} | ||
| - | + | 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. | |
| - | 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]]. | + | |
| - | + | == Equations == | |
*Variables: | *Variables: | ||
<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> | ||
| - | * | + | *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><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 /> | |
| - | + | 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> |
*The [[realmic]] [[cross-section]]s (''n'') of a dicone are: | *The [[realmic]] [[cross-section]]s (''n'') of a dicone are: | ||
<blockquote>''Unknown''</blockquote> | <blockquote>''Unknown''</blockquote> | ||
| + | |||
| + | == Cross-sections == | ||
| + | Disk-first: | ||
| + | <[#embed [hash QVCBEZBV33HTT7ST4B6DJE0CC0]]> | ||
| + | Edge-first: | ||
| + | <[#embed [hash SCYDWNKQJFQ8GJGE4JFGW8EKQD]]> | ||
| + | Cone-first: | ||
| + | <[#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: | ||
| - | <blockquote> | + | <blockquote><[#embed [hash HGY0GNY4VCYQTYW4SZVVMVD0V0]]></blockquote> |
| + | |||
| + | The nappe-first parallel projection of the dicone into 3-space is a tetrahedron. | ||
{{Tetrashapes}} | {{Tetrashapes}} | ||
| - | {{ | + | {{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 = πrh∕3 · (2r + √(r2 + h2))
bulk = π∕12 · r2h2
- The realmic cross-sections (n) of a dicone are:
Unknown
Cross-sections
Disk-first:
Edge-first:
Cone-first:
Projection
The following are the two possible types of parallel projections for a dicone:
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 | ||
