Acronym	n/2-ap
Name	n/2 antiprism
	© ©
Circumradius	sqrt[(3-2 cos(2π/n))/(8-8 cos(2π/n))]
Vertex figure	[33,n/2]   (n odd) 2[33,n/2]   (n even)
General of army	if n odd:   use a (stretched) n-p for its general if n even:   (n:2)-ap
Colonel of regiment	(is itself locally convex)
Especially	trirp (n=3)   stap (n=5)
Face vector	2n, 4n, 2n+2
Confer	n-ap   n/d-ap
External links

n=3 (trirp) would result in the retrograde triangular antiprism with height of zero, i.e. all faces would coincide. (But consider xo3/2ox&#q for a non-degenerate, taller, non-uniform variant thereof.)

For n even this looks like a double cover of a (n:2)-antiprism (with winding number 1).

Incidence matrix according to Dynkin symbol

s2sn/2s   (n>3)

demi( . .   .  ) | 2n | 1 1  2 | 1  3
-----------------+----+--------+-----
      s2s   .    ♦  2 | n *  * | 0  2
      s .   s2*a ♦  2 | * n  * | 0  2
sefa( . sn/2s  ) |  2 | * * 2n | 1  1
-----------------+----+--------+-----
      . sn/2s    ♦  n | 0 0  n | 2  *
sefa( s2sn/2s  ) |  3 | 1 1  1 | * 2n

β2βno   (n>2, odd)

both( . . .   ) | 2n | 1 1  2 | 1  3
----------------+----+--------+-----
      s2s . (r) ♦  2 | n *  * | 0  2
      s2s . (l) ♦  2 | * n  * | 0  2
sefa( . βno   ) |  2 | * * 2n | 1  1
----------------+----+--------+-----
      . βno   ) ♦  n | 0 0  n | 2  *
sefa( β2βno   ) |  3 | 1 1  1 | * 2n

or
both( . . . ) | 2n |  2  2 | 1  3
--------------+----+-------+-----
both( s2s . ) ♦  2 | 2n  * | 0  2
sefa( . βno ) |  2 |  * 2n | 1  1
--------------+----+-------+-----
      . βno   ♦  n |  0  n | 2  *
sefa( β2βno ) |  3 |  2  1 | * 2n

xon/2ox&#x   (n>3)   → height = sqrt[(1+2*cos(2pi/n))/(2+2*cos(2pi/n))]
({n/2} || dual {n/2})

o.n/2o.    | n * | 2  2 0 | 1 2 1 0
.on/2.o    | * n | 0  2 2 | 0 1 2 1
-----------+-----+--------+--------
x.   ..    | 2 0 | n  * * | 1 1 0 0
oon/2oo&#x | 1 1 | * 2n * | 0 1 1 0
..   .x    | 0 2 | *  * n | 0 0 1 1
-----------+-----+--------+--------
x.n/2o.    | n 0 | n  0 0 | 1 * * *
xo   ..&#x | 2 1 | 1  2 0 | * n * *
..   ox&#x | 1 2 | 0  2 1 | * * n *
.on/2.x    | 0 n | 0  0 n | * * * 1