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)
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(2)
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with multiplicities 12 and 4, respectively, generalized diameter
(3)
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(4)
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(5)
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(6)
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(in the orientation defined above).
The ten-of-diamonds decahedron has dihedral angles of
(7)
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(8)
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(9)
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with multiplicities 4, 4, and 8, respectively.
The ten-of-diamonds decahedron is implemented in the Wolfram Language as PolyhedronData["TenOfDiamondsDecahedron"].