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	I_h, [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.

Images

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

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	tI	ttI	atI	etI	btI	stI
Image
Net
Conway	dtI = kD kD	kdtI	jtI jtI	otI	mtI	gtI
Dual
Net

Coxeter Regular Polytopes, Third edition, (1973), Dover edition, ISBN 0-486-61480-8 (pp. 145–154 Chapter 8: Truncation)
John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5

George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input

Near-miss Johnson solids
Truncated forms	Truncated triakis tetrahedron Chamfered cube (Truncated rhombic dodecahedron) Chamfered dodecahedron (Truncated rhombic triacontahedron)
Other forms	Tetrated dodecahedron Rectified truncated icosahedron

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