Coninder (EntityTopic, 11)

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Revision as of 16:31, 28 October 2008 by Hayate (Talk | contribs)


A coninder is a special case of a tetraprism where the base is a cone. It is bounded by two cones, a cylinder, and a tetragonal torus with a degenerate hole that coincides with its single edge.

Its edge-first projection into 3-space is a cylinder containing two cones joined apex to apex by an edge.

Equations

  • Variables:
r ⇒ radius of base of coninder
h ⇒ height of coninder
l ⇒ length of coninder
total edge length = Unknown
total surface area = Unknown
surcell volume = Unknown
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

Projection

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 seems to have four cells: two cones, a cylinder and something else, which may or may not be another cylinder(?).

http://teamikaria.com/share/?caption=coninder3.png


Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus

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