Coninder (EntityTopic, 11)
From Hi.gher. Space
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Revision as of 23:09, 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 |