# Duocylinder (EntityTopic, 14)

(Difference between revisions)
 Revision as of 16:32, 18 May 2018 (view source)← Older edit Latest revision as of 08:02, 27 June 2018 (view source) Line 48: Line 48: The net of a duocylinder is two touching cylinders which have the length equal 2πr. The net of a duocylinder is two touching cylinders which have the length equal 2πr. - <[#embed [hash BTJAA2R19CVN07MM485CTG7QQB]]> + <[#embed [hash P3A8JCZSJHV3G19EZSQP28E1BA]]> - <[#embed [hash FKPYWCN700X8J0FFFF3T25EGRN]]> + <[#embed [hash GHQST8GAA0DWPGB61TJFT4ZKK7]]> == Cross-sections == == Cross-sections == Blue disk-first: Blue disk-first: - <[#embed [hash J8G4MWN5ZWWH2RAYKNB8YMFB7Z]]> + <[#embed [hash 56J0GK3126QJMFXXTZEWW6MHKC]]> Red disk-first: Red disk-first: - <[#embed [hash HFNW0J4YYBKMC29HHZC42D9W8T]]> + <[#embed [hash 4JX9MPMKTHPHJ6BWARW1JXMGXM]]> Face-first: Face-first: - <[#embed [hash 3N3EPGV8DGGRYC7M6JZ92AX4P0]]> + <[#embed [hash FN1JYDRFC5JAY1TTK3THWH2KZN]]> == Projection == == Projection ==

## Latest revision as of 08:02, 27 June 2018

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

## Net

The net of a duocylinder is two touching cylinders which have the length equal 2πr.

## Cross-sections

Blue disk-first: Red disk-first: Face-first:

## 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.

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: 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

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

 5a. (II)IICubinder 5b. ((II)II)Spheritorus 6a. (II)(II)Duocylinder 6b. ((II)(II))Tiger 7a. (III)ISpherinder 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