Acronym n-pipy
Name n-prism pyramid,
general vertex pyramid of o-3-x-3-o-n-o
Segmentochoron display
Circumradius 1/sqrt[3 - 1/sin2(π/n)]
Confer
more general:
n-pidpy  
general polytopal classes:
segmentochora  
Especially trippy (n=3)   cubpy (n=4)   pippy (n=5)   stippy (n=5/2)  

Incidence matrix according to Dynkin symbol

ox ox-n-oo&#x   (2 < n < 5.104299)   → height = sqrt[3 - 1/sin2(π/n)]/2
(pt || {n}-p)

o. o.-n-o.    | 1  *  2n 0  0 | n 2n 0 0 | n 2 0
.o .o-n-.o    | * 2n |  1 1  2 | 1  2 2 1 | 2 1 1
--------------+------+---------+----------+------
oo oo-n-oo&#x | 1  1 | 2n *  * | 1  2 0 0 | 2 1 0
.x ..   ..    | 0  2 |  * n  * | 1  0 2 0 | 2 0 1
.. .x   ..    | 0  2 |  * * 2n | 0  1 1 1 | 1 1 1
--------------+------+---------+----------+------
ox ..   ..&#x | 1  2 |  2 1  0 | n  * * * | 2 0 0
.. ox   ..&#x | 1  2 |  2 0  1 | * 2n * * | 1 1 0
.x .x   ..    | 0  4 |  0 2  2 | *  * n * | 1 0 1
.. .x-n-.o    | 0  n |  0 0  n | *  * * 2 | 0 1 1
--------------+------+---------+----------+------
ox ox   ..&#x  1  4 |  4 2  2 | 2  2 1 0 | n * *
.. ox-n-oo&#x  1  n |  n 0  n | 0  n 0 1 | * 2 *
.x .x-n-.o     0 2n |  0 n 2n | 0  0 n 2 | * * 1

{n} || n-py   → height = sqrt[3 - 3/(4 sqrt2(π/n))]/2

  n * * | 2 1 1 0 0 | 1 2 2 1 0 0 | 1 1 2 0
  * 1 *  0 n 0 n 0 | 0 n 0 n n 0 | 1 0 n 1
  * * n | 0 0 1 1 2 | 0 0 2 1 2 1 | 0 1 2 1
--------+-----------+-------------+--------
  2 0 0 | n * * * * | 1 1 1 0 0 0 | 1 1 1 0
  1 1 0 | * n * * * | 0 2 0 1 0 0 | 1 0 2 0
  1 0 1 | * * n * * | 0 0 2 1 0 0 | 0 1 2 0
  0 1 1 | * * * n * | 0 0 0 1 2 0 | 0 0 2 1
  0 0 2 | * * * * n | 0 0 1 0 1 1 | 0 1 1 1
--------+-----------+-------------+--------
  n 0 0 | n 0 0 0 0 | 1 * * * * * | 1 1 0 0
  2 1 0 | 1 2 0 0 0 | * n * * * * | 1 0 1 0
  2 0 2 | 1 0 2 0 1 | * * n * * * | 0 1 1 0
  1 1 1 | 0 1 1 1 0 | * * * n * * | 0 0 2 0
  0 1 2 | 0 0 0 2 1 | * * * * n * | 0 0 1 1
  0 0 n | 0 0 0 0 n | * * * * * 1 | 0 1 0 1
--------+-----------+-------------+--------
 n 1 0 | n n 0 0 0 | 1 n 0 0 0 0 | 1 * * *
 n 0 n | n 0 n 0 n | 1 0 n 0 0 1 | * 1 * *
 2 1 2 | 1 2 2 2 1 | 0 1 1 2 1 0 | * * n *
 0 1 n | 0 0 0 n n | 0 0 0 0 n 1 | * * * 1

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