Ditorus (EntityTopic, 11)
From Hi.gher. Space
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{{Shape|Ditorus|''No image''|4|2, 0, 0, 0|1|N/A|N/A|[[Line (object)|E]][[Circle|L]][[Torus|Q]]Q|((21)1) (((x,y),z),w)|N/A|N/A|N/A|42|N/A|N/A|pure}} | {{Shape|Ditorus|''No image''|4|2, 0, 0, 0|1|N/A|N/A|[[Line (object)|E]][[Circle|L]][[Torus|Q]]Q|((21)1) (((x,y),z),w)|N/A|N/A|N/A|42|N/A|N/A|pure}} | ||
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The '''ditorus''' is unique as it is the only [[rotope]] in four dimensions or less that has a [[pocket]]. | The '''ditorus''' is unique as it is the only [[rotope]] in four dimensions or less that has a [[pocket]]. | ||
| - | + | == Equations == | |
*Variables: | *Variables: | ||
<blockquote>''R'' ⇒ major radius of the ditorus<br> | <blockquote>''R'' ⇒ major radius of the ditorus<br> | ||
Revision as of 20:24, 22 September 2007
The ditorus is unique as it is the only rotope in four dimensions or less that has a pocket.
Equations
- Variables:
R ⇒ major radius of the ditorus
r ⇒ middle radius of the ditorus
a ⇒ minor radius of the ditorus
- All points (x, y, z, w) that lie on the surcell of a ditorus will satisfy the following equation:
(sqrt((sqrt(x2 + y2) - a)2 + z2) - r)2 + w2 = R2
- The parametric equations are:
x = (R + (r + a cos th3) cos th2) cos th1
y = (R + (r + a cos th3) cos th2) sin th1
z = (r + a cos th3) sin th2
w = a sin th3
- The hypervolumes of a ditorus are given by:
total surface area = 0
surcell volume = 8π3Rra
bulk = 4π3a2rR
- The realmic cross-sections (n) of a ditorus 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 |
