Acronym	squap
TOCID symbol	(4)Q
Name	square antiprism
	©
Circumradius	sqrt((4+sqrt(2))/8) = 0.822664
Vertex figure	[33,4]
Snub derivation
Coordinates	(1/2, 1/2, 1/sqrt(sqrt(2)))           & all changes of sign in first 2 coords (top square) (0, 1/sqrt(2), 0)           & all permutations in first 2 coords, all changes of sign in first 2 coords (bottom square)
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles (at margins)	between {3} and {3}:   arccos[(1-2 sqrt(2))/3] = 127.551603° between {3} and {4}:   arccos[(1-sqrt(2))/sqrt(3)] = 103.836160°
Face vector	8, 16, 10
Confer	more general: n-ap   n/2-ap   n/d-ap   variations: xo4ox&#q   compounds: gassic   gidsac   general polytopal classes: segmentohedra   fundamental lace prisms
External links

Incidence matrix according to Dynkin symbol

s2s4s

demi( . . . ) | 8 | 1 1 2 | 1 3
--------------+---+-------+----
      s2s .   ♦ 2 | 4 * * | 0 2
      s 2 s   ♦ 2 | * 4 * | 0 2
sefa( . s4s ) | 2 | * * 8 | 1 1
--------------+---+-------+----
      . s4s   ♦ 4 | 0 0 4 | 2 *
sefa( s2s4s ) | 3 | 1 1 1 | * 8

starting figure: x x4x

s2s8o

demi( . . . ) | 8 | 2 2 | 1 3
--------------+---+-----+----
      s2s .   ♦ 2 | 8 * | 0 2
sefa( . s8o ) | 2 | * 8 | 1 1
--------------+---+-----+----
      . s8o   ♦ 4 | 0 4 | 2 *
sefa( s2s8o ) | 3 | 2 1 | * 8

starting figure: x x8o

xo4ox&#x   → height = 1/sqrt(sqrt(2)) = 0.840896
({4} || dual {4})

o.4o.    | 4 * | 2 2 0 | 1 2 1 0
.o4.o    | * 4 | 0 2 2 | 0 1 2 1
---------+-----+-------+--------
x. ..    | 2 0 | 4 * * | 1 1 0 0
oo4oo&#x | 1 1 | * 8 * | 0 1 1 0
.. .x    | 0 2 | * * 4 | 0 0 1 1
---------+-----+-------+--------
x.4o.    | 4 0 | 4 0 0 | 1 * * *
xo ..&#x | 2 1 | 1 2 0 | * 4 * *
.. ox&#x | 1 2 | 0 2 1 | * * 4 *
.o4.x    | 0 4 | 0 0 4 | * * * 1