# Cyltrianglinder (EntityTopic, 11)

### From Hi.gher. Space

The **cyltrianglinder** is the limiting shape of an n,3-duoprism as n approaches infinity. In other words, it is the Cartesian product of a circle and a triangle. It is bounded by three cylinders and a curved cell formed by bending a triangular prism in 4D and joining the ends. Its faces are three circles and three curved faces formed by joining the ends of a rectangle in 3D.

The net of a cyltrianglinder is a triangular prism surrounded by three cylinders.

## Equations

- Variables:

r⇒ radius of the circular faces

l⇒ length of the edges in the triangles

- The hypervolumes of a cubinder are given by:

total edge length = 6πr

total surface area = 3πr(r+ 2l)

surcell volume = πr(3rl+^{√3}∕_{2}·l^{2})

bulk =^{√3}∕_{4}·πr^{2}·l^{2}

- The realmic cross-sections (
*n*) of a cyltrianglinder are:

Unknown

## Projection

The following are two possible projections of the cyltrianglinder:

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 |

19. [111]^{1}Cubic pyramid | 20. 21
^{1}Cyltrianglinder | 21. 111^{1}Triangular diprism |

List of tapertopes |