Coninder (EntityTopic, 11)

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== Projections ==
== Projections ==
The following is the parallel projection of the coninder:
The following is the parallel projection of the coninder:
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<blockquote>http://teamikaria.com/share/?caption=coninder1.png</blockquote>
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<blockquote><[#img [hash 8KB2GHFN3SBPWWMV51HWTNV6EK]]></blockquote>
In perspective projection, the coninder can also appear as two concentric cones. Note that the [[frustum]] at the bottom is actually a cylinder:
In perspective projection, the coninder can also appear as two concentric cones. Note that the [[frustum]] at the bottom is actually a cylinder:
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<blockquote>http://teamikaria.com/share/?caption=coninder2.png</blockquote>
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<blockquote><[#img [hash ND7ZR2E0QW7MRQGGDPN1G6AQV7]]></blockquote>
The following are also perspective projections of the coninder. It shows the two cones and the cylinder, with the cylindrogram collapsed into a line:
The following are also perspective projections of the coninder. It shows the two cones and the cylinder, with the cylindrogram collapsed into a line:
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<blockquote>http://teamikaria.com/share/?caption=coninder3.png</blockquote>
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<blockquote><[#img [hash D0CJPPJ3DDWZJJQS9T16M0JGN8]]></blockquote>
Its edge-first projection into 3-space is a cylinder containing two cones joined apex to apex by an edge.
Its edge-first projection into 3-space is a cylinder containing two cones joined apex to apex by an edge.

Revision as of 22:43, 8 March 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
total edge length = 4πr+l
total surface area = 2πr(r+2l+(r2+h2)2-1)
surcell volume = 2πr2(l+h3-1)
bulk = πr2hl3-1
[!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:

ExPar: [#img] is obsolete, use [#embed] instead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: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus


23. [11]2
Square dipyramid
24. 121
Coninder
25. 1[11]1
Square pyramidal prism
List of tapertopes