- Source: Small rhombihexacron
In geometry, the small rhombihexacron (or small dipteral disdodecahedron) is the dual of the small rhombihexahedron. It is visually identical to the small hexacronic icositetrahedron. Its faces are antiparallelograms formed by pairs of coplanar triangles.
Proportions
Each antiparallelogram has two angles of
arccos
(
1
4
+
1
2
2
)
≈
16.842
116
236
30
∘
{\displaystyle \arccos({\frac {1}{4}}+{\frac {1}{2}}{\sqrt {2}})\approx 16.842\,116\,236\,30^{\circ }}
and two angles of
arccos
(
−
1
2
+
1
4
2
)
≈
98.421
058
118
15
∘
{\displaystyle \arccos(-{\frac {1}{2}}+{\frac {1}{4}}{\sqrt {2}})\approx 98.421\,058\,118\,15^{\circ }}
. The diagonals of each antiparallelogram intersect at an angle of
arccos
(
1
4
+
1
8
2
)
≈
64.736
825
645
55
∘
{\displaystyle \arccos({\frac {1}{4}}+{\frac {1}{8}}{\sqrt {2}})\approx 64.736\,825\,645\,55^{\circ }}
. The dihedral angle equals
arccos
(
−
7
−
4
2
17
)
≈
138.117
959
055
51
∘
{\displaystyle \arccos({\frac {-7-4{\sqrt {2}}}{17}})\approx 138.117\,959\,055\,51^{\circ }}
. The ratio between the lengths of the long edges and the short ones equals
2
{\displaystyle {\sqrt {2}}}
.
References
Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208
External links
Weisstein, Eric W. "Small rhombihexacron". MathWorld.
Kata Kunci Pencarian:
- Daftar bentuk matematika
- Small rhombihexacron
- Icositetrahedron
- List of mathematical shapes
- Small hexacronic icositetrahedron
- List of polygons, polyhedra and polytopes
- Small rhombihexahedron
- Antiparallelogram
- List of Wenninger polyhedron models
- Great rhombihexahedron
