Loading AI tools
Near-miss Johnson solid with 92 faces From Wikipedia, the free encyclopedia
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.
Rectified truncated icosahedron | |
---|---|
![]() | |
Type | Near-miss Johnson solid |
Faces | 92: 60 isosceles triangles 12 pentagons 20 hexagons |
Edges | 180 |
Vertices | 90 |
Vertex configuration | 3.6.3.6 ![]() 3.5.3.6 ![]() |
Schläfli symbol | rt{3,5} |
Conway notation | atI[1] |
Symmetry group | Ih, [5,3], (*532) order 120 |
Rotation group | I, [5,3]+, (532), order 60 |
Dual polyhedron | Rhombic enneacontahedron |
Properties | convex |
Net | |
![]() |
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])
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.
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:
Seamless Wikipedia browsing. On steroids.
Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.
Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent.