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:

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, tetragonal trisoctahedron, strombic icositetrahedron) is a Catalan solid.