Rectified truncated icosahedron

{{Short description|Near-miss Johnson solid with 92 faces}}

{{Infobox polyhedron

| image = Rectified truncated icosahedron.png

| type = Near-miss Johnson solid

| faces = 92:
60 isosceles triangles
12 pentagons
20 hexagons

| edges = 180

| vertices = 90

| vertex_config = {{math|3.6.3.6}} 100px
{{math|3.5.3.6}} 100px

| schläfli = {{math|rt{3,5} }}

| wythoff =

| conway = {{math|atI}}{{Cite web|url=https://levskaya.github.io/polyhedronisme/?recipe=C400A1atI|title = PolyHédronisme}}

| coxeter =

| symmetry = {{math|I{{sub|h}}, [5,3], (*532)}} order 120

| rotation_group = {{math|I, [5,3]{{sup|+}}, (532),}} order 60

| dual = Rhombic enneacontahedron

| properties = convex

| vertex_figure =

| net = Rectified truncated icosahedron net.png

}}

In geometry, the rectified truncated icosahedron is a convex polyhedron. 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. The shape is a symmetrohedron with notation I(1,2,*,[2])