Great triambic icosahedron

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 = 60
V = 32 (χ = -8)
F = 20, E = 60
V = 24 (χ = -16)
Isohedral faces
Duals
Great ditrigonal icosidodecahedron

Ditrigonal dodecadodecahedron
Stellation
Icosahedron: W34

Stellation diagram
3D model of a medial triambic icosahedron
3D model of a 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. These figures can be differentiated by marking 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. Alternatively, if the faces are filled with the even–odd rule, the internal structure of both shapes will differ.

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