Coninder (EntityTopic, 11)
From Hi.gher. Space
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- | A '''coninder''' is a special case of a [[ | + | 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]]. |
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== Equations == | == Equations == | ||
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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 = 4πr+l<br> |
- | total surface area = | + | total surface area = 2πr(r+2l+(r<sup>2</sup>+h<sup>2</sup>)<sup>2<sup>-1</sup></sup>)<br> |
- | surcell volume = | + | surcell volume = 2πr<sup>2</sup>(l+h3<sup>-1</sup>)<br> |
bulk = πr<sup>2</sup>hl3<sup>-1</sup></blockquote> | bulk = πr<sup>2</sup>hl3<sup>-1</sup></blockquote> | ||
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[!w] ⇒ cone of base radius ''r'' and height ''h''</blockquote> | [!w] ⇒ cone of base radius ''r'' and height ''h''</blockquote> | ||
- | == | + | == Projections == |
The following is the parallel projection of the coninder: | The following is the parallel projection of the coninder: | ||
<blockquote>http://teamikaria.com/share/?caption=coninder1.png</blockquote> | <blockquote>http://teamikaria.com/share/?caption=coninder1.png</blockquote> | ||
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<blockquote>http://teamikaria.com/share/?caption=coninder2.png</blockquote> | <blockquote>http://teamikaria.com/share/?caption=coninder2.png</blockquote> | ||
- | The following are also perspective projections of the coninder. It | + | The following are also perspective projections of the coninder. It shows the two cones and the cylinder, with the cylindrogram collapsed into a line: |
<blockquote>http://teamikaria.com/share/?caption=coninder3.png</blockquote> | <blockquote>http://teamikaria.com/share/?caption=coninder3.png</blockquote> | ||
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+ | Its edge-first projection into 3-space is a cylinder containing two cones joined apex to apex by an edge. | ||
{{Tetrashapes}} | {{Tetrashapes}} | ||
{{Rotope Nav|36|37|38|((II)II)<br>Toracubinder|(II)'I<br>Coninder|<nowiki>(II)''</nowiki><br>Dicone|chora}} | {{Rotope Nav|36|37|38|((II)II)<br>Toracubinder|(II)'I<br>Coninder|<nowiki>(II)''</nowiki><br>Dicone|chora}} |
Revision as of 23:07, 5 November 2008
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)2-1)
surcell volume = 2πr2(l+h3-1)
bulk = πr2hl3-1
- The realmic cross-sections (n) of a coninder are:
[!x,!y] ⇒ Unknown
[!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:
http://teamikaria.com/share/?caption=coninder1.png
In perspective projection, the coninder can also appear as two concentric cones. Note that the frustum at the bottom is actually a cylinder:
http://teamikaria.com/share/?caption=coninder2.png
The following are also perspective projections of the coninder. It shows the two cones and the cylinder, with the cylindrogram collapsed into a line:
http://teamikaria.com/share/?caption=coninder3.png
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 |