Coninder (EntityTopic, 11)
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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 == | ||
+ | Cylinder-first: | ||
+ | <[#embed [hash QSS6E66KT1FJPFEQP8Z3GZ9JCK]]> | ||
+ | Cone-first: | ||
+ | <[#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.
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 + √(r^{2} + h^{2}))
surcell volume = πr(^{2rh}∕_{3} + l(r + √(r^{2} + h^{2})))
bulk = ^{π}∕_{3} · r^{2}hl
- The realmic cross-sections (n) of a coninder are:
[!x,!y] ⇒ isosceles triangular prism of base length 2r, perpendicular height h and length l
[!z] ⇒ cylinder of radius (r − ^{nr}∕_{h}) and height l
[!w] ⇒ cone of base radius r and height h
Cross-sections
Cylinder-first: Cone-first: Round face-first:
Projections
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: | 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 |
23. [11]^{2} Square dipyramid | 24. 12^{1} Coninder | 25. 1[11]^{1} Square pyramid prism |
List of tapertopes |