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 great deltoidal icositetrahedron (or great sagittal disdodecahedron) is the dual of the

nonconvex great rhombicuboctahedron In geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17. It has 26 faces (8 triangles and 18 squares), 48 edges, and 24 vertices. It is represented by the Schläfli symbol rr and Coxeter-Dynkin dia ...

. Its faces are darts. Part of each dart lies inside the solid, hence is invisible in solid models. One of its halves can be rotated by 45 degrees to form the pseudo great deltoidal icositetrahedron, analogous to the pseudo-deltoidal icositetrahedron.

Proportions

Faces have three angles of

\arccos(\frac+\frac\sqrt)\approx 31.399\,714\,809\,92^

and one of

360^-\arccos(-\frac+\frac\sqrt)\approx 265.800\,855\,570\,24^

. Its

dihedral angles 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 uni ...

equal

\arccos()\approx 94.531\,580\,798\,20^

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

2+\frac\sqrt\approx 2.707\,106\,781\,19

References

External links

Dual uniform polyhedra {{Polyhedron-stub