Torinder (EntityTopic, 11)

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{{Shape|Torinder|''No image''|4|?, ?, ?, 0|1|N/A|N/A|[[Line (object)|E]][[Circle|L]][[Torus|Q]]E|(21)1 ((x,y),z),w|N/A|N/A|N/A}}
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<[#ontology [kind topic] [cats 4D Curved Toratope]]>
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{{STS Shape
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| name=Torinder
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| dim=4
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| elements=?, ?, ?, 0
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| genus=1
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| ssc=[x[(yz)w]T]
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| ssc2=+T((2)1)
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| extra={{STS Toratope
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| expand=[[Duocyldyinder|221]]
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| notation=((II)I)I
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| index=8a
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}}}}
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== Geometry ==
 
A '''torinder''' is the linear extension of a [[torus]].
A '''torinder''' is the linear extension of a [[torus]].
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=== Equations ===
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== Equations ==
*Variables:
*Variables:
<blockquote>''R'' ⇒ major radius of the torinder<br>
<blockquote>''R'' ⇒ major radius of the torinder<br>
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*The [[realmic]] [[cross-section]]s (''n'') of a torinder are:
*The [[realmic]] [[cross-section]]s (''n'') of a torinder are:
<blockquote>''Unknown''</blockquote>
<blockquote>''Unknown''</blockquote>
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<br clear="all"><br>
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{{Tetrashapes}}
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{{Polychora}}
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{{Toratope Nav A|7|8|9|(III)I<br>Spherinder|((III)I)<br>Torisphere|((II)I)I<br>Torinder|(((II)I)I)<br>Ditorus|IIIII<br>Penteract|(IIIII)<br>Pentasphere|chora}}
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{{Rotopes}}
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Latest revision as of 19:53, 2 February 2014


A torinder is the linear extension of a torus.

Equations

  • Variables:
R ⇒ major radius of the torinder
r ⇒ minor radius of the torinder
h ⇒ height of the torinder
  • All points (x, y, z, w) that lie on the surcell of a torinder will satisfy the following equation:
h ≥ |w|
r2 = (sqrt(x2 + y2) - R)2 + z2
x = (R + r cos(θ)) cos(Φ)
y = (R + r cos(θ)) sin(Φ)
z = r sin(θ)
w = w
surface area of margin = 8π2Rr
surcell volume = 4πRr(πr + h)
bulk = 2π2Rr2h
Unknown


Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus


7a. (III)I
Spherinder
7b. ((III)I)
Torisphere
8a. ((II)I)I
Torinder
8b. (((II)I)I)
Ditorus
9a. IIIII
Penteract
9b. (IIIII)
Pentasphere
List of toratopes