Coninder (EntityTopic, 11)

(Difference between revisions)
 Revision as of 20:49, 11 February 2014 (view source)Hayate (Talk | contribs)m (K6.4 upgrade: img -> embed)← Older edit Latest revision as of 18:15, 24 April 2018 (view source) Line 32: Line 32: [!z] ⇒ [[cylinder]] of radius (''r'' − {{Over|''nr''|''h''}}) and height ''l''
[!z] ⇒ [[cylinder]] of radius (''r'' − {{Over|''nr''|''h''}}) and height ''l''
[!w] ⇒ cone of base radius ''r'' and height ''h'' [!w] ⇒ cone of base radius ''r'' and height ''h'' + + == 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
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

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