Polyhedron with 24 faces
3D model of a 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
External links
Weisstein, Eric W. "Small rhombihexacron" . MathWorld .