Coninder (EntityTopic, 11)
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| - | {{Shape|Coninder| | + | <[#ontology [kind topic] [cats 4D Curved Tapertope]]> |
| - | = | + | {{STS Shape |
| - | + | | attrib=pure | |
| + | | name=Coninder | ||
| + | | dim=4 | ||
| + | | elements=4, 5, 3, 2 | ||
| + | | genus=0 | ||
| + | | ssc=[x(yz)P] | ||
| + | | ssc2=+&T2 | ||
| + | | extra={{STS Tapertope | ||
| + | | order=2, 1 | ||
| + | | notation=12<sup>1</sup> | ||
| + | | index=24 | ||
| + | }}}} | ||
| - | + | 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: | *Variables: | ||
<blockquote>''r'' ⇒ radius of base of coninder<br> | <blockquote>''r'' ⇒ radius of base of coninder<br> | ||
| Line 11: | Line 23: | ||
*The [[hypervolume]]s of a coninder are given by: | *The [[hypervolume]]s of a coninder are given by: | ||
| - | <blockquote>total edge length = '' | + | <blockquote>total edge length = 4π''r'' + ''l''<br> |
| - | total surface area = '' | + | total surface area = 2π''r''(''r'' + 2''l'' + √(''r''<sup>2</sup> + ''h''<sup>2</sup>))<br> |
| - | surcell volume = '' | + | surcell volume = π''r''({{Over|2''rh''|3}} + ''l''(''r'' + √(''r''<sup>2</sup> + ''h''<sup>2</sup>)))<br> |
| - | + | bulk = {{Over|π|3}} · ''r''<sup>2</sup>''hl''</blockquote> | |
*The [[realmic]] [[cross-section]]s (''n'') of a coninder are: | *The [[realmic]] [[cross-section]]s (''n'') of a coninder are: | ||
| - | <blockquote>[!x,!y] ⇒ '' | + | <blockquote>[!x,!y] ⇒ isosceles [[triangular prism]] of base length 2''r'', perpendicular height ''h'' and length ''l''<br> |
| - | [!z] ⇒ [[cylinder]] of radius (''r'' | + | [!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 == | ||
| + | The following is the parallel projection of the coninder: | ||
| + | <blockquote><[#embed [hash 8KB2GHFN3SBPWWMV51HWTNV6EK]]></blockquote> | ||
| + | |||
| + | In perspective projection, the coninder can also appear as two concentric cones. Note that the [[frustum]] at the bottom is actually a cylinder: | ||
| + | <blockquote><[#embed [hash ND7ZR2E0QW7MRQGGDPN1G6AQV7]]></blockquote> | ||
| + | |||
| + | The following are also perspective projections of the coninder. It shows the two cones and the cylinder, with the cylindrogram collapsed into a line: | ||
| + | <blockquote><[#embed [hash D0CJPPJ3DDWZJJQS9T16M0JGN8]]></blockquote> | ||
| + | |||
| + | Its edge-first projection into 3-space is a cylinder containing two cones joined apex to apex by an edge. | ||
| + | |||
| + | {{Tetrashapes}} | ||
| + | {{Tapertope Nav|23|24|25|[11]<sup>2</sup><br>Square dipyramid|12<sup>1</sup><br>Coninder|1[11]<sup>1</sup><br>Square pyramid prism|chora}} | ||
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 + √(r2 + h2))
surcell volume = πr(2rh∕3 + l(r + √(r2 + h2)))
bulk = π∕3 · r2hl
- 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. 121 Coninder | 25. 1[11]1 Square pyramid prism |
| List of tapertopes | ||
