Tridiminished icosahedron | |
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Type | Johnson J62 – J63 – J64 |
Faces | 5 triangles 3 pentagons |
Edges | 15 |
Vertices | 9 |
Vertex configuration | |
Symmetry group | |
Properties | convex, non-composite |
Net | |
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In geometry, the tridiminished icosahedron is a Johnson solid that is constructed by removing three pentagonal pyramids from a regular icosahedron.
The tridiminished icosahedron can be constructed by removing three regular pentagonal pyramid from a regular icosahedron. [1] The aftereffect of such construction leaves five equilateral triangles and three regular pentagons. [2] Since all of its faces are regular polygons and the resulting polyhedron remains convex, the tridiminished icosahedron is a Johnson solid, and it is enumerated as the sixty-third Johnson solid . [3] This construction is similar to other Johnson solids as in gyroelongated pentagonal pyramid and metabidiminished icosahedron. [1]
The tridiminished icosahedron is a non-composite polyhedron: there is no plane that intersects its surface only in edges, so that it cannot be thereby divided into two or more regular or Johnson polyhedra. [4]
The surface area of a tridiminished icosahedron is the sum of all polygonal faces' area: five equilateral triangles and three regular pentagons. Its volume can be ascertained by subtracting the volume of a regular icosahedron from the volume of three pentagonal pyramids. Given that is the edge length of a tridiminished icosahedron, they are: [2]
A tridiminished icosahedron has three kinds of dihedral angles. These angles are between two triangles: 138.1°, triangle to pentagon: 100.8°, and two pentagons: 63.4°. [5]
The tridiminished icosahedron is a vertex figure of a 4-polytope, a snub 24-cell. [6]