# Triangular diprism (EntityTopic, 16)

A triangular diprism is a special case of the prism where the base is a triangular prism. It is also a duoprism with parameters of 3 and 4.

## Equations

• Variables:
l ⇒ length of each line in the triangular diprism
total edge length = 24l
total surface area = (15 + 2√3) · l2
surcell volume = (3 + 2√3) · l3
bulk = √32 · l4
[!x,!y] ⇒ cuboid with a various size
[!z,!w] ⇒ triangular prism

## Net

The net of a triangular diprism is three cubes with four triangular prisms attached to the middle cube:

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## Projection

The parallel projection of a triangular diprism is the following: ## Incidence matrix

 # TXID Type Name Va Ea Eb 3a 4a 4b C1a C2a 0 Va = point ; 1 Ea 2 = digon ; blue 2 Eb 2 = digon ; black 3 3a 3 3 0 = triangle ; joins 2 triangular prisms 4 4a 4 0 4 = square ; joins 2 cubes 5 4b 4 2 2 = square ; joins triangular prism to cube 6 C1a 6 6 3 2 0 3 = base of prism: triangular prism ; 7 C2a 8 4 8 0 2 4 = cube ; 8 H4.1a 12 12 12 4 3 12 4 3 = triangular diprism ;

## Usage as facets

 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

 20. 211Cyltrianglinder 21. 1111Triangular diprism 22. 22Dicone List of tapertopes