Deltoidal icositetrahedron

Deltoidal icositetrahedron
(rotating and 3D model)
Type	Catalan
Conway notation	oC or deC
Coxeter diagram
Face polygon	Kite with 3 equal acute angles & 1 obtuse angle
Faces	24, congruent
Edges	24 short + 24 long = 48
Vertices	8 (connecting 3 short edges) + 6 (connecting 4 long edges) + 12 (connecting 4 alternate short & long edges) = 26
Face configuration	V3.4.4.4
Symmetry group	Oh, BC3, [4,3], *432
Rotation group	O, [4,3]+, (432)
Dihedral angle	same value for short & long edges: ${\displaystyle \arccos \left(-{\frac {7+4{\sqrt {2}}}{17}}\right)}$ ${\displaystyle \approx 138^{\circ }07'05''}$
Dual polyhedron	Rhombicuboctahedron
Properties	convex, face-transitive
Net

D.i. as artwork and die

D.i. projected onto cube and octahedron in Perspectiva Corporum Regularium

Dyakis dodecahedron crystal model and projection onto octahedron

In geometry, the deltoidal icositetrahedron (or trapezoidal icositetrahedron, tetragonal icosikaitetrahedron,^[1] tetragonal trisoctahedron,^[2] strombic icositetrahedron) is a Catalan solid. Its 24 faces are congruent kites.^[3] The deltoidal icositetrahedron, whose dual is the (uniform) rhombicuboctahedron, is tightly related to the pseudo-deltoidal icositetrahedron, whose dual is the pseudorhombicuboctahedron; but the actual and pseudo-d.i. are not to be confused with each other.