Square antiprism

{{Infobox polytope The square antiprism, or squap, is a prismatic uniform polyhedron. It consists of 8 triangles and 2 squares. Each vertex joins one square and three triangles. As the name suggests, it is an antiprism based on a square.
 * dim = 3
 * obsa = Squap
 * img=Square antiprism.png
 * 3d=Square antiprism.stl
 * type=Uniform
 * coxeter = s2s4s
 * symmetry = BC2×A1+
 * army=Squap
 * reg=Squap
 * faces = 8 triangles, 2 squares
 * edges = 8+8
 * vertices = 8
 * circum = $\sqrt{(4+√2)/8}$ ≈ 0.82267
 * volume = {{radic4+3$\sqrt{2}$}}/3 ≈ 0.95700
 * verf = {{Trapezoid]], edge lengths 1, 1, 1, $\sqrt{2}$
 * dih= 3–3: acos(–(2$\sqrt{2}$–1)/3) ≈ 127.55160º
 * dih2=4–3: acos(–($\sqrt{6}$–$\sqrt{3}$)/3) ≈ 103.83616º
 * dual = Square trapezohedron
 * conjugate = Squaree antiprism
 * conv=Yes
 * orient=Yes
 * nat=Tame}}

Vertex coordinates
A square antiprism of edge length 1 has vertex coordinates given bycc
 * (±1/2, ±1/2, $\sqrt{2√2}$/4),
 * (0, ±$\sqrt{2}$/2, –$\sqrt{2√2}$/4),
 * (±$\sqrt{2}$/2, 0, –$\sqrt{2√2}$/4).