Ten-of-Diamonds Decahedron

The ten-of-diamonds decahedron is a stereohedron and space-filling polyhedron on 8 vertices, 16 edges, and 10 faces (8 of which are non-equilateral triangles and two of which are rhombi). Because it is polyhedron with 10 faces including two opposite diamond-shaped faces, Goldberg (1982, Fig. 10-II) named it after the "ten of diamonds" playing card.

The ten-of-diamonds decahedron can be defined as the convex hull of the eight points , , , and , giving a solid with short edge length .

The net of the ten-of-diamonds decahedron is illustrated above.

A ten-of-diamonds decahedron has edge lengths

			(1)
			(2)

with multiplicities 12 and 4, respectively, generalized diameter

(3)

surface area

(4)

volume

(5)

and moment of inertia

(6)

(in the orientation defined above).

The ten-of-diamonds decahedron has dihedral angles of

			(7)
			(8)
			(9)

with multiplicities 4, 4, and 8, respectively.

The ten-of-diamonds decahedron is implemented in the Wolfram Language as PolyhedronData["TenOfDiamondsDecahedron"].