Duocylinder

Duocylinder
Rank	4
Notation
Tapertopic notation	22
Toratopic notation	(II)(II)
Bracket notation	[(II)(II)]
Elements
Cells	2 tori
Faces	1 Clifford torus
Measures (edge length 1)
Circumradius	$\sqrt2r$
Volume	$\pi^2r^4$
Related polytopes
Dual	Duospindle
Conjugate	None
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	O(2)≀S2
Convex	Yes

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 $\pi^2a^2b^2$.

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

• $x^2+y^2 = z^2+w^2 = r^2.$

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

• $x^2+y^2 < z^2+w^2 = r^2,$
• $z^2+w^2 < x^2+y^2 = r^2.$

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

• $x^2+y^2<r^2 \quad\text{and}\quad z^2+w^2<r^2.$

External links

• Wikipedia Contributors. "Duocylinder".
• Hi.gher.Space Wiki Contributors. "Duocylinder".

• Quickfur. "The Duocylinder".