Torinder (EntityTopic, 11)
From Hi.gher. Space
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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}} | + | {{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|40}} |
== Geometry == | == Geometry == | ||
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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> | ||
| - | |||
{{Polychora}} | {{Polychora}} | ||
| - | {{ | + | {{Rotope Nav|39|40|41|((II)'I)<br>Conic torus|((II)I)I<br>Torinder|((II)I)'<br>Toric pyramid}} |
Revision as of 13:00, 17 June 2007
Geometry
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
