The small triambic icosahedron is the dual polyhedron of the small ditrigonal icosidodecahedron ,
and is Wenninger model . It can be constructed by augmentation
of a unit edge-length icosahedron by a pyramid with
height ,
giving a solid with edge lengths and 1.

Wenninger (1989, p. 49) calls this solid the triakis octahedron (which is a term more commonly used for the dual of one of the Archimedean solids).

It is implemented in the Wolfram Language
as PolyhedronData ["SmallTriambicIcosahedron" ].

The convex hull of the small ditrigonal icosidodecahedron is a regular dodecahedron
whose dual is the icosahedron , so the dual of the
small ditrigonal icosidodecahedron
(i.e., the small triambic icosahedron) is one of the icosahedron
stellations (Wenninger 1983, p. 42). In fact, it is the second icosahedron
stellation in the enumeration of Maeder (1994).

The small triambic icosahedron has 32 vertices, 90 edges, and 70 faces. Its vertices are arranged in two concentric groups of 12 (indicated in red in the above illustration) and 20 (blue).

For a small triambic icosahedron with edge lengths

the vertices determine a regular icosahedron and
regular dodecahedron with circumradii

respectively.

The solid in the right figure is the dodecahedron-small
triambic icosahedron compound .

The surface area and volume
of the small triambic icosahedron are

The solid small triambic icosahedron has moment of inertia tensor

(7)

for uniform density solid of mass .

See also Dodecahedron-Small Triambic Icosahedron Compound ,

Dual Polyhedron ,

Echidnahedron ,

Great
Triakis Octahedron ,

Icosahedron Stellations ,

Small Ditrigonal Icosidodecahedron ,

Small Triakis Octahedron ,

Triakis
Icosahedron ,

Explore with Wolfram|Alpha
References Maeder, R. E. "The Stellated Icosahedra."
Mathematica in Education 3 , 5-11, 1994. http://library.wolfram.com/infocenter/Articles/2519/ .Wenninger,
M. J. Dual
Models. Cambridge, England: Cambridge University Press, pp. 42 and 46-47
1983. Wenninger, M. J. Polyhedron
Models. New York: Cambridge University Press, p. 46, 1989.
Cite this as:
Weisstein, Eric W. "Small Triambic Icosahedron."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/SmallTriambicIcosahedron.html

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