Icositetrahedron

In geometry, an icositetrahedron[1] refers to a polyhedron with 24 faces, none of which are regular polyhedra.

However, many are composed of regular polygons, such as the triaugmented dodecahedron and the disphenocingulum.

Some icositetrahedra are near-spherical, but are not composed of regular polygons.

A minimum of 14 vertices is required to form a icositetahedron.

[2] There are many symmetric forms, and the ones with highest symmetry have chiral icosahedral symmetry: Four Catalan solids, convex: 27 uniform star-polyhedral duals: (self-intersecting) Examples with lower symmetry include certain dual polyhedra of Johnson solids , such as the gyroelongated square bicupola and the elongated square gyrobicupola.

Common examples include prisms and pyramids, and include certain Johnson solids and Catalan solids.

Every vertex borders 2 squares and an icosidigon base.

, its Schläfli symbol is {22}×{} or t{2,22}, its Coxeter diagram is , and its Conway polyhedron notation is P22.

Every vertex borders 2 triangles and a hendecagon base.

Dodecagonal trapezohedra are the tenth member of the trapezohedra family, made of 24 congruent kites arranged radially.

Every dodecagonal trapezohedron has 24 faces, 28 edges, and 26 vertices.

[5] Its Schläfli symbol is { }⨁{12}, its Coxeter diagram is or , and its Conway polyhedron notation is dA12.

They are listed as follows: 4 squares 9 pentagons There are 5 types of icositetrahedra with different topologies.

[6] The pentagonal icositetetrahedron has two mirror images (enantiomorphs), so geometrically there are 4 distinct Catalan icositetetrahedra.