Coninder (EntityTopic, 11)

From Hi.gher. Space

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<[#ontology [kind topic] [cats 4D Curved Tapertope]]>
{{STS Shape
{{STS Shape
| attrib=pure
| attrib=pure
| name=Coninder
| name=Coninder
| dim=4
| dim=4
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| elements=4, ?, ?, ?
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| elements=4, 5, 3, 2
| genus=0
| genus=0
| ssc=[x(yz)P]
| ssc=[x(yz)P]
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| extra={{STS Rotope
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| ssc2=+&T2
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| attrib=pure
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| extra={{STS Tapertope
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| notation=2<sup>1</sup>1
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| order=2, 1
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| index=37
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| notation=12<sup>1</sup>
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| index=24
}}}}
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A '''coninder''' is a special case of a [[tetraprism]] where the base is a [[cone]]. It is bounded by two cones, a cylinder, and a tetragonal torus with a degenerate hole that coincides with its single edge.
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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]].
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Its edge-first projection into 3-space is a cylinder containing two cones joined apex to apex by an edge.
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== Equations ==
== Equations ==
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*The [[hypervolume]]s of a coninder are given by:
*The [[hypervolume]]s of a coninder are given by:
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<blockquote>total edge length = ''Unknown''<br>
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<blockquote>total edge length = ''r'' + ''l''<br>
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total surface area = ''Unknown''<br>
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total surface area = ''r''(''r'' + 2''l'' + √(''r''<sup>2</sup> + ''h''<sup>2</sup>))<br>
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surcell volume = ''Unknown''<br>
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surcell volume = π''r''({{Over|2''rh''|3}} + ''l''(''r'' + √(''r''<sup>2</sup> + ''h''<sup>2</sup>)))<br>
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bulk = πr<sup>2</sup>hl3<sup>-1</sup></blockquote>
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bulk = {{Over|π|3}} &middot; ''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:
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<blockquote>[!x,!y] ⇒ ''Unknown''<br>
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<blockquote>[!x,!y] ⇒ isosceles [[triangular prism]] of base length 2''r'', perpendicular height ''h'' and length ''l''<br>
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[!z] ⇒ [[cylinder]] of radius (''r''-''rnh''<sup>-1</sup>) and height ''l''<br>
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[!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>
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== Projection ==
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== Cross-sections ==
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Cylinder-first:
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<[#embed [hash QSS6E66KT1FJPFEQP8Z3GZ9JCK]]>
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Cone-first:
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<[#embed [hash G8BM88NQ9ST4JFZP9TM8RZZEYH]]>
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Round face-first:
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<[#embed [hash K4ESA41DFANJTM7H97CCCBDJ35]]>
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== Projections ==
The following is the parallel projection of the coninder:
The following is the parallel projection of the coninder:
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<blockquote>http://fusion-global.org/share/coninder1.png</blockquote>
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<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:
In perspective projection, the coninder can also appear as two concentric cones. Note that the [[frustum]] at the bottom is actually a cylinder:
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<blockquote>http://fusion-global.org/share/coninder2.png</blockquote>
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<blockquote><[#embed [hash ND7ZR2E0QW7MRQGGDPN1G6AQV7]]></blockquote>
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The following are also perspective projections of the coninder. It seems to have four cells: two cones, a cylinder and something else, which may or may not be another cylinder{{hmm}}.
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The following are also perspective projections of the coninder. It shows the two cones and the cylinder, with the cylindrogram collapsed into a line:
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<blockquote>http://fusion-global.org/share/coninder3.png</blockquote>
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<blockquote><[#embed [hash D0CJPPJ3DDWZJJQS9T16M0JGN8]]></blockquote>
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Its edge-first projection into 3-space is a cylinder containing two cones joined apex to apex by an edge.
{{Tetrashapes}}
{{Tetrashapes}}
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{{Rotope Nav|36|37|38|((II)II)<br>Toracubinder|(II)'I<br>Coninder|<nowiki>(II)''</nowiki><br>Dicone|chora}}
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{{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
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: (image) Cone-first: (image) Round face-first: (image)

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: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus


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