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Snub cube information


Snub cube

(Click here for rotating model)
Type Archimedean solid
Uniform polyhedron
Elements F = 38, E = 60, V = 24 (χ = 2)
Faces by sides (8+24){3}+6{4}
Conway notation sC
Schläfli symbols sr{4,3} or
ht0,1,2{4,3}
Wythoff symbol | 2 3 4
Coxeter diagram
Symmetry group O, 1/2B3, [4,3]+, (432), order 24
Rotation group O, [4,3]+, (432), order 24
Dihedral angle 3-3: 153°14′04″ (153.23°)
3-4: 142°59′00″ (142.98°)
References U12, C24, W17
Properties Semiregular convex chiral

Colored faces

3.3.3.3.4
(Vertex figure)

Pentagonal icositetrahedron
(dual polyhedron)

Net
A geometric construction of the Tribonacci constant (AC), with compass and marked ruler, according to the method described by Xerardo Neira.
3D model of a snub cube

In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles. It has 60 edges and 24 vertices.

It is a chiral polyhedron; that is, it has two distinct forms, which are mirror images (or "enantiomorphs") of each other. The union of both forms is a compound of two snub cubes, and the convex hull of both sets of vertices is a truncated cuboctahedron.

Kepler first named it in Latin as cubus simus in 1619 in his Harmonices Mundi. H. S. M. Coxeter, noting it could be derived equally from the octahedron as the cube, called it snub cuboctahedron, with a vertical extended Schläfli symbol , and representing an alternation of a truncated cuboctahedron, which has Schläfli symbol .

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Snub cube

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In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles. It has 60 edges and 24...

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Archimedean solid

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square gyrobicupola; 15 if the mirror images of two enantiomorphs, the snub cube and snub dodecahedron, are counted separately). Here the vertex configuration...

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Pentagonal icositetrahedron

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pentagonal icosikaitetrahedron is a Catalan solid which is the dual of the snub cube. In crystallography it is also called a gyroid. It has two distinct forms...

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List of mathematical shapes

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Compound of two inverted snub dodecadodecahedra Compound of two small stellated dodecahedra Compound of two snub cubes Compound of two snub dodecadodecahedra...

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Cube

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In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meeting at each vertex. Viewed from a...

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Catalan solid

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icositetrahedron and the pentagonal hexecontahedron, dual to the chiral snub cube and snub dodecahedron. These each come in two enantiomorphs. Not counting the...

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Cuboctahedron

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Pseudocuboctahedron Rhombicuboctahedron Truncated cuboctahedron Tetradecahedron Snub cube Notice that the cuboctahedron has four hexagonal central planes, inclined...

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Snub polyhedron

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snub cube: Snub polyhedra have Wythoff symbol | p q r and by extension, vertex configuration 3.p.3.q.3.r. Retrosnub polyhedra (a subset of the snub polyhedron...

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Truncated cuboctahedron

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to a nonuniform snub cube with chiral octahedral symmetry, a nonuniform rhombicuboctahedron with pyritohedral symmetry (the cantic snub octahedron) and...

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Snub octahedron

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Snub octahedron may refer to: Icosahedron, with pyritohedral symmetry, s { 3 , 4 } {\displaystyle s{\begin{Bmatrix}3,4\end{Bmatrix}}} , Snub cube, or...

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Cubic honeycomb

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(with Th symmetry), snub cubes, two kinds of cubes: square prisms and rectangular trapezoprisms (topologically equivalent to a cube but with D2d symmetry)...

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Snub rhombicuboctahedron

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also be called the Conway snub cuboctahedron in but will be confused with the Coxeter snub cuboctahedron, the snub cube. The snub rhombicuboctahedron can...

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Compound of two snub cubes

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uniform polyhedron compound is a composition of the 2 enantiomers of the snub cube. As a holosnub, it is represented by Schläfli symbol βr{4,3} and Coxeter...

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Regular icosahedron

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same rotations as the tetrahedron, and are somewhat analogous to the snub cube and snub dodecahedron, including some forms which are chiral and some with...

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Rhombicuboctahedron

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is an Archimedean solid. The polyhedron has octahedral symmetry, like the cube and octahedron. Its dual is called the deltoidal icositetrahedron or trapezoidal...

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Icosahedron

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up as a lower pyritohedral symmetry, and is called a snub octahedron, snub tetratetrahedron, snub tetrahedron, and pseudo-icosahedron. This can be seen...

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Runcinated tesseracts

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given Coxeter diagram , and symmetry [4,3,3]+, and constructed from 8 snub cubes, 16 icosahedra, 24 square antiprisms, 32 octahedra (as triangular antiprisms)...

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List of numbers

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first centered square number besides 1 that is also a square number. 27, the cube of 3, the value of 33. 28, the second perfect number. 30, the smallest sphenic...

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Noble polyhedron

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2008, Robert Webb discovered a new noble polyhedron, a faceting of the snub cube. This was the first new class of noble polyhedra (with chiral octahedral...

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