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])
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and 20 regular hexagons. It is constructed as a rectified, truncatedicosahedron, rectification truncating vertices down to mid-edges. As a near-miss Johnson...
great icosahedron, produces a sequence of uniform polyhedra. Truncating edges down to points produces the great icosidodecahedron as a rectified great...
four rectified compact regular honeycombs: The truncated icosahedral honeycomb, t0,1{3,5,3}, , has alternating dodecahedron and truncatedicosahedron cells...
the great icosahedron. The truncated great stellated dodecahedron is a degenerate polyhedron, with 20 triangular faces from the truncated vertices, and...
the rhombic triacontahedron. It can also be seen as a nonuniform truncatedicosahedron with pyramids augmented to the pentagonal and hexagonal faces with...
The icosidodecahedron is a rectified dodecahedron and also a rectifiedicosahedron, existing as the full-edge truncation between these regular solids...
all triangular faces to be equilateral. Truncated tetrahedron: The four faces from the tetrahedron are truncated to become regular hexagons, and there are...
{5}}-1)E^{3}} It shares the same edge arrangement as the convex regular icosahedron; the compound with both is the small complex icosidodecahedron. If only...
into an icosahedron, octahedron, and tetrahedron by folding along the diagonals of its square sides. With Oh symmetry, order 48, it is a rectified cube or...
in dimensional series 22k. The rectified 221 has 216 vertices, and 126 facets: 72 rectified 5-simplices, and 27 rectified 5-orthoplexes and 27 5-demicubes...
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