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Ten-of-Diamonds Decahedron


TenOfDiamondsDecahedron

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 (0,+/-2,-1), (+/-2,0,1), (+/-1,0,-1), and (0,+/-1,1), giving a solid with short edge length sqrt(5).

TenOfDiamondsDecahedronNet

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

A ten-of-diamonds decahedron has edge lengths

s_1=a
(1)
s_2=2asqrt(3/5)
(2)

with multiplicities 12 and 4, respectively, generalized diameter

 d=(4a)/(sqrt(5)),
(3)

surface area

 S=8/5(1+sqrt(6))a^2,
(4)

volume

 V=(32)/(15sqrt(5))a^3,
(5)

and moment of inertia

 I=[(31)/(200) 0 0; 0 (31)/(200) 0; 0 0 1/(19)100]Ma^2
(6)

(in the orientation defined above).

The ten-of-diamonds decahedron has dihedral angles of

alpha_1=cos^(-1)(-2/3)
(7)
alpha_2=(2pi)/3
(8)
alpha_3=sec^(-1)(-sqrt(6))
(9)

with multiplicities 4, 4, and 8, respectively.

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


See also

Decahedron, Space-Filling Polyhedra, Stereohedron

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References

Goldberg, M. "On the Space-Filling Decahedra." Structural Topology, No. 7, pp. 39-44, 1982.Koch, E. Wirkungsbereichspolyeder und Wirkungsbereichsteilunger zukubischen Gitterkomplexen mit weniger als drei Freiheitsgraden. Dissertation. Marburg, Germany: University Marburg/Lahn, 1972.

Cite this as:

Weisstein, Eric W. "Ten-of-Diamonds Decahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Ten-of-DiamondsDecahedron.html

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