Great disdyakis dodecahedron

Template:Short description Template:Uniform polyhedra db File:Great disdyakis dodecahedron.stl In geometry, the great disdyakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform great truncated cuboctahedron. It has 48 triangular faces.

Proportions

The triangles have one angle of $\arccos (\frac{3}{4}+\frac{1}{8}\sqrt{2})\approx 22.06219115754^{\circ }$, one of $\arccos (-\frac{1}{6}-\frac{1}{12}\sqrt{2})\approx 106.53002715022^{\circ }$ and one of $\arccos (-\frac{1}{12}+\frac{1}{2}\sqrt{2})\approx 51.40778169224^{\circ }$. The dihedral angle equals $\arccos (\frac{-71+12\sqrt{2}}{97})\approx 123.84889157944^{\circ }$. Part of each triangle lies within the solid, hence is invisible in solid models.

Related polyhedra

The great disdyakis dodecahedron is topologically identical to the convex Catalan solid, disdyakis dodecahedron, which is dual to the truncated cuboctahedron.

References

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External links

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