# Great triambic icosahedron

In geometry, the great triambic icosahedron and medial triambic icosahedron (or midly triambic icosahedron) are visually identical dual uniform polyhedra. The exterior surface also represents the De2f2 stellation of the icosahedron. The only way to differentiate these two polyhedra is to mark which intersections between edges are true vertices and which are not. In the above images, true vertices are marked by gold spheres, which can be seen in the concave Y-shaped areas.

 Great triambic icosahedron Medial triambic icosahedron Types Dual uniform polyhedra Symmetry group Ih Name Great triambic icosahedron Medial triambic icosahedron Index references DU47, W34, 30/59 DU41, W34, 30/59 Elements F = 20, E = 60V = 32 (χ = -8) F = 20, E = 60V = 24 (χ = -16) Isohedral faces Duals Great ditrigonal icosidodecahedron Ditrigonal dodecadodecahedron Stellation Icosahedron: W34 Stellation diagram

The 12 vertices of the convex hull matches the vertex arrangement of an icosahedron.

## Great triambic icosahedron

The great triambic icosahedron is the dual of the great ditrigonal icosidodecahedron, U47. It has 20 inverted-hexagonal (triambus) faces, shaped like a three-bladed propeller. It has 32 vertices: 12 exterior points, and 20 hidden inside. It has 60 edges.

## Medial triambic icosahedron

The medial triambic icosahedron is the dual of the ditrigonal dodecadodecahedron, U41. It has 20 faces, each being simple concave isogonal hexagons or triambi. It has 24 vertices: 12 exterior points, and 12 hidden inside. It has 60 edges.

Unlike the great triambic icosahedron, the medial triambic icosahedron is topologically a regular polyhedron of index two. By distorting the triambi into regular hexagons, one obtains a quotient space of the hyperbolic order-5 hexagonal tiling:

## As a stellation

It is Wenninger's 34th model as his 9th stellation of the icosahedron