Triamond antiprism 2,2

Triamond antiprism 2,2
Rank	3
Type	Convex triamond polyhedron
Elements
Faces	1 square, 2 trapezoids, 2 triangles
Edges	1+2+2+4
Vertices	2+4
Measures (minor edge length 1)
Volume	${\dfrac {\sqrt {2}}{3}}\approx 0.47140$
Surface area	$2{\sqrt {3}}+1\approx 4.46410$
Central density	1
Number of external pieces	5
Level of complexity	9
Abstract & topological properties
Flag count	36
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Convex	Yes
Nature	Tame
History
Discovered by	Roger Kaufman

The triamond antiprism 2,2 is a convex triamond polyhedron. It can be made by augmenting a square pyramid with two tetrahedra on opposite triangular faces and combining co-planar faces in the result, or as a section of the triangular cupola.

It has the fewest vertices, faces and edges of any known convex triamond polyhedron.

Related polytopes

Disection of a triangular cupola into convex triamond polyhedra. Red (left) is a triamond triangular cupola section and blue (right) is a triamond antiprism 2,2.

The triamond antiprism 2,2 can be augmented with itself along its rhombic face to form another convex triamond polyhedron.

The triamond antiprism 2,2 can augment a triamond triangular cupola section to form the triangular cupola.

External links

• Kaufman, Roger. "Convex Triamond Regular Polyhedra."