| Tridiminished icosahedron | |
|---|---|
 | |
| Type | Johnson J62 – J63 – J64 |
| Faces | 5 triangles 3 pentagons |
| Edges | 15 |
| Vertices | 9 |
| Vertex configuration | |
| Symmetry group | |
| Properties | convex, non-composite |
| Net | |
 | |
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 non-composite polyhedron, meaning it is convex polyhedron that cannot be separated by a plane into two or more regular polyhedrons. [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 with the volume of three pentagonal pyramids. Given that is the edge length of a tridiminished icosahedron, they are: [2]
In geometry, the regular icosahedron is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two pentagonal pyramids with regular faces to each of its pentagonal faces, or by putting points onto the cube. The resulting polyhedron has 20 equilateral triangles as its faces, 30 edges, and 12 vertices. It is an example of a Platonic solid and of a deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron.
In geometry, an icosidodecahedron or pentagonal gyrobirotunda is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such, it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.
In geometry, an octahedron is a polyhedron with eight faces. An octahedron can be considered as a square bipyramid. When the edges of a square bipyramid are all equal in length, it produces a regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. It is also an example of a deltahedron. An octahedron is the three-dimensional case of the more general concept of a cross polytope.
In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.
In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges.
The triaugmented triangular prism, in geometry, is a convex polyhedron with 14 equilateral triangles as its faces. It can be constructed from a triangular prism by attaching equilateral square pyramids to each of its three square faces. The same shape is also called the tetrakis triangular prism, tricapped trigonal prism, tetracaidecadeltahedron, or tetrakaidecadeltahedron; these last names mean a polyhedron with 14 triangular faces. It is an example of a deltahedron, composite polyhedron, and Johnson solid.
In geometry, the pentagonal bipyramid is a polyhedron with 10 triangular faces. It is constructed by attaching two pentagonal pyramids to each of their bases. If the triangular faces are equilateral, the pentagonal bipyramid is an example of deltahedra, composite polyhedron, and Johnson solid.
In geometry, the gyroelongated pentagonal pyramid is a polyhedron constructed by attaching a pentagonal antiprism to the base of a pentagonal pyramid. An alternative name is diminished icosahedron because it can be constructed by removing a pentagonal pyramid from a regular icosahedron.
In geometry, pentagonal pyramid is a pyramid with a pentagon base and five triangular faces, having a total of six faces. It is categorized as Johnson solid if all of the edges are equal in length, forming equilateral triangular faces and a regular pentagonal base. The pentagonal pyramid can be found in many polyhedrons, including their construction. It also occurs in stereochemistry in pentagonal pyramidal molecular geometry.
In geometry, the elongated square cupola is a polyhedron constructed from an octagonal prism by attaching square cupola onto its base. It is an example of Johnson solid.
In geometry, the pentagonal cupola is one of the Johnson solids. It can be obtained as a slice of the rhombicosidodecahedron. The pentagonal cupola consists of 5 equilateral triangles, 5 squares, 1 pentagon, and 1 decagon.
In geometry, the hebesphenomegacorona is a Johnson solid with 18 equilateral triangles and 3 squares as its faces.
In geometry, the sphenomegacorona is a Johnson solid with 16 equilateral triangles and 2 squares as its faces.
In geometry, the triangular hebesphenorotunda is a Johnson solid with 13 equilateral triangles, 3 squares, 3 regular pentagons, and 1 regular hexagon, making the total of its faces is 20.
In geometry, the elongated triangular pyramid is one of the Johnson solids. As the name suggests, it can be constructed by elongating a tetrahedron by attaching a triangular prism to its base. Like any elongated pyramid, the resulting solid is topologically self-dual.
In geometry, the elongated pentagonal bipyramid is a polyhedron constructed by attaching two pentagonal pyramids onto the base of a pentagonal prism. It is an example of Johnson solid.
In geometry, the augmented triangular prism is a polyhedron constructed by attaching an equilateral square pyramid onto the square face of a triangular prism. As a result, it is an example of Johnson solid. It can be visualized as the chemical compound, known as capped trigonal prismatic molecular geometry.
In geometry, the biaugmented triangular prism is a polyhedron constructed from a triangular prism by attaching two equilateral square pyramids onto two of its square faces. It is an example of Johnson solid. It can be found in stereochemistry in bicapped trigonal prismatic molecular geometry.
In geometry, the augmented pentagonal prism is a polyhedron that can be constructed by attaching an equilateral square pyramid onto the square face of pentagonal prism. It is an example of Johnson solid.
In geometry, the biaugmented pentagonal prism is a polyhedron constructed from a pentagonal prism by attaching two equilateral square pyramids onto each of its square faces. It is an example of Johnson solid.
