Torinder (EntityTopic, 11)
From Hi.gher. Space
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- | {{Shape|Torinder| | + | <[#ontology [kind topic] [cats 4D Curved Toratope]]> |
+ | {{STS Shape | ||
+ | | name=Torinder | ||
+ | | dim=4 | ||
+ | | elements=?, ?, ?, 0 | ||
+ | | genus=1 | ||
+ | | ssc=[x[(yz)w]T] | ||
+ | | ssc2=+T((2)1) | ||
+ | | extra={{STS Toratope | ||
+ | | expand=[[Duocyldyinder|221]] | ||
+ | | notation=((II)I)I | ||
+ | | index=8a | ||
+ | }}}} | ||
- | |||
A '''torinder''' is the linear extension of a [[torus]]. | A '''torinder''' is the linear extension of a [[torus]]. | ||
- | + | == Equations == | |
*Variables: | *Variables: | ||
<blockquote>''R'' ⇒ major radius of the torinder<br> | <blockquote>''R'' ⇒ major radius of the torinder<br> | ||
Line 27: | Line 38: | ||
*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> | ||
- | + | {{Tetrashapes}} | |
- | {{ | + | {{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}} |
- | {{ | + |
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
- The parametric equations are:
x = (R + r cos(θ)) cos(Φ)
y = (R + r cos(θ)) sin(Φ)
z = r sin(θ)
w = w
- The hypervolumes of a torinder are given by:
surface area of margin = 8π2Rr
surcell volume = 4πRr(πr + h)
bulk = 2π2Rr2h
- The realmic cross-sections (n) of a torinder are:
Unknown
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 |
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 |