Square antiprismatic prism
Encyclopedia
| Square antiprismatic prism | |
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 Schlegel diagram |
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| Type | Uniform antiprismatic prism Uniform antiprismatic prism In 4-dimensional geometry, a uniform antiprismatic prism is a uniform polychoron with two uniform antiprism cells in two parallel 3-space hyperplanes, connected by uniform prisms cells between pairs of faces.... |
| Schläfli symbol | s{2,4}x{} |
| Coxeter-Dynkin Coxeter-Dynkin diagram In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors... |
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| Cells | 2 (3.3.3.4 Square antiprism In geometry, the square antiprism is the second in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps... )  8 (3.4.4 Triangular prism In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.... )  2 4.4.4 Cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and... |
| Faces | 16 {3} Triangle A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted .... , 16 {4} Square (geometry) In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles... , 4 p-gons Regular polygon A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:... |
| Edges | 40 |
| Vertices | 16 |
| Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:... |
irregular quadrilateral pyramid |
| Symmetry group Coxeter notation In geometry, Coxeter notation is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group. It uses a bracketed notation, with modifiers to indicate certain subgroups. The notation is named after H. S. M... |
[(3,4)+,2] |
| Properties | convex Convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn... |
In geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a square antiprismatic prism is a convex uniform
Uniform polychoron
In geometry, a uniform polychoron is a polychoron or 4-polytope which is vertex-transitive and whose cells are uniform polyhedra....
polychoron
Polychoron
In geometry, a polychoron or 4-polytope is a four-dimensional polytope. It is a connected and closed figure, composed of lower dimensional polytopal elements: vertices, edges, faces , and cells...
(four dimensional polytope). It is formed as two parallel square antiprism
Square antiprism
In geometry, the square antiprism is the second in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps...
s connected by cubes and triangular prisms.
Related polytopes
It is the second in an infinite series of uniform antiprismatic hyperprisms. The first is the triangular antiprism prism, which is also an octahedral prismOctahedral prism
In geometry, a octahedral prism is a convex uniform polychoron . This polychoron has 10 polyhedral cells: 2 octahedra connected by 8 triangular prisms.- Related polytopes :...
.