Duocylinder

Duocylinder
Rank4
Notation
Tapertopic notation22
Toratopic notation(II)(II)
Bracket notation[(II)(II)]
Elements
Cells2 tori
Faces1 Clifford torus
Measures (edge length 1)
Circumradius${\displaystyle \sqrt2r}$
Volume${\displaystyle \pi^2r^4}$
Related polytopes
DualDuospindle
ConjugateNone
Abstract & topological properties
OrientableYes
Properties
SymmetryO(2)≀S2
ConvexYes

A duocylinder is the Cartesian product of two disks. It is the limit of the n,m-duoprisms as n and m approach infinity, and also the limit of the n-gonal prisminders as n approaches infinity. Its surface consists of two identical tori.

It is a rotatope, thus it is also a toratope, a tapertope, and a bracketope.

Variations of the duocylinder exist where the base circles have different radii. Then the volume is ${\displaystyle \pi^2a^2b^2}$.

Coordinates

Where r is the minor radius of one of the cells:

Points on the face of a duocylinder are all points (x,y,z,w) such that

• ${\displaystyle x^2+y^2 = z^2+w^2 = r^2.}$

Points on the surcell of a duocylinder are all points (x,y,z,w) such that

• ${\displaystyle x^2+y^2 < z^2+w^2 = r^2,}$
• ${\displaystyle z^2+w^2 < x^2+y^2 = r^2.}$

Points in the interior of a duocylinder are all points (x,y,z,w) such that

• ${\displaystyle x^2+y^2