Acronym	n-appy
Name	n-antiprismatical pyramid
Segmentochoron display
Circumradius	sqrt[(2-2 cos(π/n))/(5-6 cos(π/n))]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Face vector	2n+1, 6n, 6n+2, 2n+3
Especially	pen (n=2)*   octpy (n=3)   squappy (n=4)   pappy (n=5)   stapepy (n=5/2)
Confer	related concept: n-apt   general polytopal classes: segmentochora

* The case n=2 equally would be considerable here by concept, it just has a different incidence matrix as the n-gons become degenerate.

Note the conceptual difference between this antiprism-pyramid and the pyramid-antiprism n-apt. In fact, the latter happens to be the external blend of 2 of the former.

Solving the height formula below for the limitting (then degenerate) case, results in n ≤ π/arccos(5/6) = 5.363958.

Incidence matrix

pt || n-ap   → height = sqrt[(5-6 cos(π/n))/(8-8 cos(π/n))]

1  * ♦ 2n  0  0 | 2n 2n 0  0 | 2 2n 0
* 2n |  1  2  2 |  2  2 1  3 | 1  3 1
-----+----------+------------+-------
1  1 | 2n  *  * |  2  2 0  0 | 1  3 0
0  2 |  * 2n  * |  1  0 1  1 | 1  1 1
0  2 |  *  * 2n |  0  1 0  2 | 0  2 1
-----+----------+------------+-------
1  2 |  2  1  0 | 2n  * *  * | 1  1 0
1  2 |  2  0  1 |  * 2n *  * | 0  2 0
0  n |  0  n  0 |  *  * 2  * | 1  0 1  {n}
0  3 |  0  1  2 |  *  * * 2n | 0  1 1
-----+----------+------------+-------
1  n |  n  n  0 |  n  0 1  0 | 2  * *  n-py
1  3 |  3  1  2 |  1  2 0  1 | * 2n *  tet
0 2n |  0 2n 2n |  0  0 2 2n | *  * 1  n-ap