Duocylinder (EntityTopic, 14)

From Higher Dimensions Database


A duocylinder is the Cartesian product of two circles, and is therefore the square of the circle. It is also the limit of the set of m,n-duoprisms as m and n tend to infinity.

Equations

  • Variables:
a ⇒ radius of the circle in the xy plane
b ⇒ radius of the circle in the zw plane
  • All points (x, y, z, w) that lie on the sole 2D face of a duocylinder will satisfy the following equations:
x2 + y2 = a2
z2 + w2 = b2
  • A duocylinder has two cells which meet at the 2D face. These are given respectively by the systems of equations:
  1. x2 + y2 = a2; z2 + w2b2
  2. x2 + y2a2; z2 + w2 = b2
  • Each of these bounding volumes are topologically equivalent to the inside of a 3D torus. The set of points (w,x,y,z) that satisfy either the first or the second set of equations constitute the surface of the duocylinder.
total surface area = 4π2ab
surcell volume = 2π2ab(a + b)
bulk = π2a2b2

Projection

The perspective projection of a duocylinder is the following shape. The purple part is one cell, and the black part is the other cell.

(image)

In a parallel projection, both cells collapse to cylinders, one capped and one uncapped, resulting in a single cylinder being observed as the projection.


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


13. 31
Spherinder
14. 22
Duocylinder
15. 211
Cubinder
List of tapertopes


5a. (II)II
Cubinder
5b. ((II)II)
Spheritorus
6a. (II)(II)
Duocylinder
6b. ((II)(II))
Tiger
7a. (III)I
Spherinder
7b. ((III)I)
Torisphere
List of toratopes


27. (<(II)I>I)
Biconic crind
28. [(II)(II)]
Duocylinder
29. <(II)(II)>
Duocircular tegum
List of bracketopes