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It is also sometimes called a trisoctahedron, or, more fully, trigonal trisoctahedron.
The tetragonal trisoctahedron is another name for the deltoidal icositetrahedron, a different polyhedron with three quadrilateral faces for every face of an octahedron.
(Nicol and Goldschmidt 1903) identified seventeen crystal forms exhibited by sperrylite, including four different trapezohedra, a trisoctahedron, five pyritohedra, and four diploids.