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Some polyhedra with 24 faces include:

A triaugmented dodecahedron, which consists of 15 triangular faces and 9 pentagonal faces.
A disphenocingulum, which consists of 20 triangular faces and 4 quadrilateral faces.
A triakis octahedron, which consists of 24 triangular faces.
A tetrakis hexahedron, otherwise known as a disdyakis cube, which consists of 24 triangular faces - the appearance of a cube on the inside, with six pyramidal faces on each cubic face.
A trapezoidal icositetrahedron, which consists of 24 quadrilateral faces.
And a pentagonal icositetrahedron, which consists of 24 pentagonal faces.

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Some polyhedra with 24 faces include:

A triaugmented dodecahedron, which consists of 15 triangular faces and 9 pentagonal faces.
A disphenocingulum, which consists of 20 triangular faces and 4 quadrilateral faces.
A triakis octahedron, which consists of 24 triangular faces.
A tetrakis hexahedron, otherwise known as a disdyakis cube, which consists of 24 triangular faces - the appearance of a cube on the inside, with six pyramidal faces on each cubic face.
A trapezoidal icositetrahedron, which consists of 24 quadrilateral faces.
And a pentagonal icositetrahedron, which consists of 24 pentagonal faces.

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