Coninder (EntityTopic, 11)

From Hi.gher. Space

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[!z] ⇒ [[cylinder]] of radius (''r'' − {{Over|''nr''|''h''}}) and height ''l''<br>
[!z] ⇒ [[cylinder]] of radius (''r'' − {{Over|''nr''|''h''}}) and height ''l''<br>
[!w] ⇒ cone of base radius ''r'' and height ''h''</blockquote>
[!w] ⇒ cone of base radius ''r'' and height ''h''</blockquote>
== Cross-sections ==
<[#embed [hash QSS6E66KT1FJPFEQP8Z3GZ9JCK]]>
<[#embed [hash G8BM88NQ9ST4JFZP9TM8RZZEYH]]>
Round face-first:
<[#embed [hash K4ESA41DFANJTM7H97CCCBDJ35]]>
== Projections ==
== Projections ==

Latest revision as of 18:15, 24 April 2018

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.


  • 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


Cylinder-first: (image) Cone-first: (image) Round face-first: (image)


The following is the parallel projection of the coninder:


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


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


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
25. 1[11]1
Square pyramid prism
List of tapertopes