Coninder (EntityTopic, 11)
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*The [[hypervolume]]s of a coninder are given by: | *The [[hypervolume]]s of a coninder are given by: | ||
- | <blockquote>total edge length = | + | <blockquote>total edge length = 4π''r'' + ''l''<br> |
- | total surface area = | + | total surface area = 2π''r''(''r'' + 2''l'' + √(''r''<sup>2</sup> + ''h''<sup>2</sup>))<br> |
- | surcell volume = | + | surcell volume = π''r''({{Over|2''rh''|3}} + ''l''(''r'' + √(''r''<sup>2</sup> + ''h''<sup>2</sup>)))<br> |
- | bulk = | + | bulk = {{Over|π|3}} · ''r''<sup>2</sup>''hl''</blockquote> |
*The [[realmic]] [[cross-section]]s (''n'') of a coninder are: | *The [[realmic]] [[cross-section]]s (''n'') of a coninder are: | ||
- | <blockquote>[!x,!y] ⇒ '' | + | <blockquote>[!x,!y] ⇒ isosceles [[triangular prism]] of base length 2''r'', perpendicular height ''h'' and length ''l''<br> |
[!z] ⇒ [[cylinder]] of radius (''r''-''rnh''<sup>-1</sup>) and height ''l''<br> | [!z] ⇒ [[cylinder]] of radius (''r''-''rnh''<sup>-1</sup>) and height ''l''<br> | ||
[!w] ⇒ cone of base radius ''r'' and height ''h''</blockquote> | [!w] ⇒ cone of base radius ''r'' and height ''h''</blockquote> |
Revision as of 15:54, 18 November 2011
A coninder is a special case of a prism where the base is a cone. It is bounded by two cones, a cylinder and a cylindrogram.
Equations
- Variables:
r ⇒ radius of base of coninder
h ⇒ height of coninder
l ⇒ length of coninder
- The hypervolumes of a coninder are given by:
total edge length = 4πr + l
total surface area = 2πr(r + 2l + √(r2 + h2))
surcell volume = πr(2rh∕3 + l(r + √(r2 + h2)))
bulk = π∕3 · r2hl
- The realmic cross-sections (n) of a coninder are:
[!x,!y] ⇒ isosceles triangular prism of base length 2r, perpendicular height h and length l
[!z] ⇒ cylinder of radius (r-rnh-1) and height l
[!w] ⇒ cone of base radius r and height h
Projections
The following is the parallel projection of the coninder:
ExPar: [#img] is obsolete, use [#embed] instead
In perspective projection, the coninder can also appear as two concentric cones. Note that the frustum at the bottom is actually a cylinder:
ExPar: [#img] is obsolete, use [#embed] instead
The following are also perspective projections of the coninder. It shows the two cones and the cylinder, with the cylindrogram collapsed into a line:
ExPar: [#img] is obsolete, use [#embed] instead
Its edge-first projection into 3-space is a cylinder containing two cones joined apex to apex by an edge.
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 |
23. [11]2 Square dipyramid | 24. 121 Coninder | 25. 1[11]1 Square pyramidal prism |
List of tapertopes |