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°
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
wikipedia   mathworld   quickfur

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

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