This
uniform polyhedron compound
In geometry, a uniform polyhedron compound is a polyhedral compound whose constituents are identical (although possibly enantiomorphous) uniform polyhedra, in an arrangement that is also uniform, i.e. the symmetry group of the compound acts t ...
is a composition of the 2
enantiomers
In chemistry, an enantiomer (Help:IPA/English, /ɪˈnænti.əmər, ɛ-, -oʊ-/ Help:Pronunciation respelling key, ''ih-NAN-tee-ə-mər''), also known as an optical isomer, antipode, or optical antipode, is one of a pair of molecular entities whi ...
of the
snub dodecahedron
In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex Isogonal figure, isogonal nonprismatic solids constructed by two or more types of regular polygon Face (geometry), faces.
The snub dod ...
.
The
vertex arrangement
In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes.
For example, a ''square vertex arrangement'' is understood to mean four points in a plane, equa ...
of this compound is shared by a convex nonuniform
truncated icosidodecahedron
In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron,Wenninger Model Number 16 great rhombicosidodecahedron,Williams (Section 3-9, p. 94)Cromwell (p. 82) omnitruncated dodecahedron or omnitruncated icosahedronNorman Wooda ...
, with rectangular faces, alongside irregular
hexagon
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.
Regular hexagon
A regular hexagon is de ...
s and
decagon
In geometry, a decagon (from the Greek δέκα ''déka'' and γωνία ''gonía,'' "ten angles") is a ten-sided polygon or 10-gon.. The total sum of the interior angles of a simple decagon is 1440°. Regular decagon
A '' regular decagon'' has a ...
s, each alternating two different edge lengths.
Together with its convex hull, it represents the snub dodecahedron-first projection of the nonuniform
snub dodecahedral antiprism.
See also
*
Compound of two icosahedra
This uniform polyhedron compound is a composition of 2 icosahedra. It has octahedral symmetry ''Oh''. As a holosnub, it is represented by Schläfli symbol β and Coxeter diagram .
The triangles in this compound decompose into two orbits under a ...
*
Compound of two snub cubes
This uniform polyhedron compound is a composition of the 2 enantiomers of the snub cube. As a holosnub, it is represented by Schläfli symbol βr and Coxeter diagram .
The vertex arrangement of this compound is shared by a convex nonuniform t ...
References
*.
Polyhedral compounds
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