# Rectified truncated icosahedron

Rectified truncated icosahedron
Schläfli symbol rt{3,5}
Conway notation atI[1]
Faces 92:
60 { }∨( )
12 {5}
20 {6}
Edges 180
Vertices 90
Vertex figures 3.6.3.6
3.5.3.6
Symmetry group Ih, [5,3], (*532) order 120
Rotation group I, [5,3]+, (532), order 60
Dual polyhedron Rhombic enneacontahedron
Properties convex

Net

The rectified truncated icosahedron is a polyhedron, constructed as a rectified truncated icosahedron. It has 92 faces: 60 isosceles triangles, 12 regular pentagons, and 20 regular hexagons. It is constructed as a rectified truncated icosahedron, rectification truncating vertices down to mid-edges.

As a near-miss Johnson solid, under icosahedral symmetry, the pentagons are always regular, although the hexagons, while having equal edge lengths, do not have the same edge lengths with the pentagons, having slightly different but alternating angles, causing the triangles to be isosceles instead.

## Dual

By Conway polyhedron notation, the dual polyhedron can be called a joined truncated icosahedron, jtI, but it is topologically equivalent to the rhombic enneacontahedron with all rhombic faces.

## Related polyhedra

The rectified truncated icosahedron can be seen in sequence of rectification and truncation operations from the truncated icosahedron. Further truncation, and alternation operations creates two more polyhedra:

Name Truncated
icosahedron
Truncated
truncated
icosahedron
Rectified
truncated
icosahedron
Expanded
truncated
icosahedron
Truncated
rectified
truncated
icosahedron
Snub
rectified
truncated
icosahedron
Coxeter tI ttI rtI rrtI trtI srtI
Conway atI etI btI stI
Image
Net
Conway dtI = kD kD kdtI jtI jtI otI mtI gtI
Dual
Net