- Source: Great disdyakis dodecahedron
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
(
3
4
+
1
8
2
)
≈
22.062
191
157
54
∘
{\displaystyle \arccos({\frac {3}{4}}+{\frac {1}{8}}{\sqrt {2}})\approx 22.062\,191\,157\,54^{\circ }}
, one of
arccos
(
−
1
6
−
1
12
2
)
≈
106.530
027
150
22
∘
{\displaystyle \arccos(-{\frac {1}{6}}-{\frac {1}{12}}{\sqrt {2}})\approx 106.530\,027\,150\,22^{\circ }}
and one of
arccos
(
−
1
12
+
1
2
2
)
≈
51.407
781
692
24
∘
{\displaystyle \arccos(-{\frac {1}{12}}+{\frac {1}{2}}{\sqrt {2}})\approx 51.407\,781\,692\,24^{\circ }}
. The dihedral angle equals
arccos
(
−
71
+
12
2
97
)
≈
123.848
891
579
44
∘
{\displaystyle \arccos({\frac {-71+12{\sqrt {2}}}{97}})\approx 123.848\,891\,579\,44^{\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
Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208
External links
Weisstein, Eric W. "Great disdyakis dodecahedron". MathWorld.
Kata Kunci Pencarian:
- Daftar bentuk matematika
- Great disdyakis dodecahedron
- Disdyakis dodecahedron
- Disdyakis triacontahedron
- Dodecahedron
- List of mathematical shapes
- List of polygons, polyhedra and polytopes
- Tetrakis hexahedron
- Great rhombihexahedron
- 25 great circles of the spherical octahedron
- Deltoidal icositetrahedron
