geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, the small rhombidodecacron is a nonconvex isohedral polyhedron. It is the

dual Dual or Duals may refer to: Paired/two things * Dual (mathematics), a notion of paired concepts that mirror one another ** Dual (category theory), a formalization of mathematical duality *** see more cases in :Duality theories * Dual (grammatical ...

of the small rhombidodecahedron. It is visually identical to the Small dodecacronic hexecontahedron. It has 60 intersecting antiparallelogram faces.

Proportions

Each face has two angles of

\arccos(\frac+\frac\sqrt)\approx 25.242\,832\,961\,52^

and two angles of

\arccos(-\frac+\frac\sqrt)\approx 93.025\,844\,508\,96^

. The diagonals of each antiparallelogram intersect at an angle of

\arccos(\frac+\frac\sqrt)\approx 61.731\,322\,529\,52^

. The ratio between the lengths of the long edges and the short ones equals

\frac+\frac\sqrt

, which is the

golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( ...

. The

dihedral angle A dihedral angle is the angle between two intersecting planes or half-planes. In chemistry, it is the clockwise angle between half-planes through two sets of three atoms, having two atoms in common. In solid geometry, it is defined as the un ...

equals

\arccos(\frac)\approx 154.121\,363\,125\,78^

References

External links

*
Uniform polyhedra and duals
Dual uniform polyhedra {{polyhedron-stub