Coninder (EntityTopic, 11)

From Higher Dimensions Database


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))
surcell volume = πr(2rh3 + l(r + √(r2 + h2)))
bulk = π3 · r2hl
[!x,!y] ⇒ isosceles triangular prism of base length 2r, perpendicular height h and length l
[!z] ⇒ cylinder of radius (rnrh) and height l
[!w] ⇒ cone of base radius r and height h

Projections

The following is the parallel projection of the coninder:

(image)

In perspective projection, the coninder can also appear as two concentric cones. Note that the frustum at the bottom is actually a cylinder:

(image)

The following are also perspective projections of the coninder. It shows the two cones and the cylinder, with the cylindrogram collapsed into a line:

(image)

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: glomecubinderduocylinderspherindersphonediconeconinder
Torii: tigertorispherespheritorustorinderditorus


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