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,[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.
^Conway, Symmetries of Things, p. 284–286.
^"Keyword: "forms" | ClipArt ETC".
^"Kite". Retrieved 6 October 2019.
and 23 Related for: Deltoidal icositetrahedron information
In geometry, the great deltoidalicositetrahedron (or great sagittal disdodecahedron) is the dual of the nonconvex great rhombicuboctahedron. Its faces...
the cube and octahedron. Its dual is called the deltoidalicositetrahedron or trapezoidal icositetrahedron, although its faces are not really true trapezoids...
(the stella octangula). This trend continues on with the deltoidalicositetrahedron and deltoidal hexecontahedron for the dual pairings of the other regular...
{\displaystyle q=r} , rhombi. Applying this, for example, to the deltoidalicositetrahedron ( p = 4 {\displaystyle p=4} , q = 3 {\displaystyle q=3} and r...
rhombicuboctahedron, which is not a uniform polyhedron. The great deltoidalicositetrahedron is the dual of the nonconvex great rhombicuboctahedron. Maeder...
triangle. Deltoidalicositetrahedron Each face is a kite. Pseudo-deltoidalicositetrahedron Each face is a kite. Pentagonal icositetrahedron Each face...
dodecahedron /ˈdʌɪəkɪsˌdəʊdɪkəˈhiːdrən/ or diploid is a variant of the deltoidalicositetrahedron with pyritohedral symmetry, transforming the kite faces into chiral...
octahedron. The tetragonal trisoctahedron is another name for the deltoidalicositetrahedron, a different polyhedron with three quadrilateral faces for every...
triangle type and 3 square types. The deltoidalicositetrahedron has 1 face type. The pseudo-deltoidalicositetrahedron has 2 face types, with same shape...
dodecahedron Kisrhombille tiling Compound of three octahedra Deltoidalicositetrahedron, another 24-face Catalan solid. Hexakistetraeder in German, see...
tiling and its dual triangular tiling, which shares its edges with the deltoidal trihexagonal tiling. The Euclidean compounds of two hypercubic honeycombs...
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