The pentagonal icositetrahedron is the 24-faced dual polyhedron of the snub cube. It is illustrated above
together with a wireframe version and a net that can be used
for its construction.

The mineral cuprite () forms in pentagonal icositetrahedral crystals (Steinhaus
1999, pp. 207 and 209).

It is Wenninger dual .

Because it is the dual of the chiralsnub cube, the pentagonal icositetrahedron also comes in two enantiomorphous
forms, known as laevo (left) and dextro (right). An attractive dual of the two enantiomers
superposed on one another is illustrated above.

A cube, octahedron, and stella octangula can all be inscribed on the vertices of the pentagonal icositetrahedron (E. Weisstein,
Dec. 25, 2009).

Surprisingly, the tribonacci constant
is intimately related to the metric properties of the pentagonal icositetrahedron
cube.

Its irregular pentagonal faces have vertex angles of