Acronym	pippy, K-4.141
Name	pentagonal-prismatic pyramid, vertex pyramid of the rectified hexacosachoron
Segmentochoron display
Circumradius	sqrt[5+2 sqrt(5)] = 3.077684
Dihedral angles	at {3} between squippy and squippy:   arccos[-(1+3 sqrt(5))/8] = 164.477512° at {3} between peppy and squippy:   arccos(-sqrt[7+3 sqrt(5)]/4) = 157.761244° at {5} between peppy and pip:   18° at {4} between pip and squippy:   arccos(sqrt[(5+2 sqrt(5))/10]) = 13.282526°
Face vector	11, 25, 22, 8
Confer	general pyramids: pt || n-p   uniform relative: rox   general polytopal classes: segmentochora
External links

As abstract polytope pippy is isomorphic to stippy, thereby replacing pentagons by pentagrams resp. replacing pip by stip and peppy by stappy.

Incidence matrix according to Dynkin symbol

ox ox5oo&#x   → height = sqrt[(5-2 sqrt(5))/20] = 0.162460
(pt || pip)

o. o.5o.    | 1  * ♦ 10 0  0 | 5 10 0 0 | 5 2 0
.o .o5.o    | * 10 |  1 1  2 | 1  2 2 1 | 2 1 1
------------+------+---------+----------+------
oo oo5oo&#x | 1  1 | 10 *  * | 1  2 0 0 | 2 1 0
.x .. ..    | 0  2 |  * 5  * | 1  0 2 0 | 2 0 1
.. .x ..    | 0  2 |  * * 10 | 0  1 1 1 | 1 1 1
------------+------+---------+----------+------
ox .. ..&#x | 1  2 |  2 1  0 | 5  * * * | 2 0 0
.. ox ..&#x | 1  2 |  2 0  1 | * 10 * * | 1 1 0
.x .x ..    | 0  4 |  0 2  2 | *  * 5 * | 1 0 1
.. .x5.o    | 0  5 |  0 0  5 | *  * * 2 | 0 1 1
------------+------+---------+----------+------
ox ox ..&#x ♦ 1  4 |  4 2  2 | 2  2 1 0 | 5 * *
.. ox5oo&#x ♦ 1  5 |  5 0  5 | 0  5 0 1 | * 2 *
.x .x5.o    ♦ 0 10 |  0 5 10 | 0  0 5 2 | * * 1

{5} || peppy   → height = (sqrt(5)-1)/4 = 0.309017

  5 * * | 2 1 1 0 0 | 1 2 2 1 0 0 | 1 1 2 0
  * 1 * ♦ 0 5 0 5 0 | 0 5 0 5 5 0 | 1 0 5 1
  * * 5 | 0 0 1 1 2 | 0 0 2 1 2 1 | 0 1 2 1
--------+-----------+-------------+--------
  2 0 0 | 5 * * * * | 1 1 1 0 0 0 | 1 1 1 0
  1 1 0 | * 5 * * * | 0 2 0 1 0 0 | 1 0 2 0
  1 0 1 | * * 5 * * | 0 0 2 1 0 0 | 0 1 2 0
  0 1 1 | * * * 5 * | 0 0 0 1 2 0 | 0 0 2 1
  0 0 2 | * * * * 5 | 0 0 1 0 1 1 | 0 1 1 1
--------+-----------+-------------+--------
  5 0 0 | 5 0 0 0 0 | 1 * * * * * | 1 1 0 0
  2 1 0 | 1 2 0 0 0 | * 5 * * * * | 1 0 1 0
  2 0 2 | 1 0 2 0 1 | * * 5 * * * | 0 1 1 0
  1 1 1 | 0 1 1 1 0 | * * * 5 * * | 0 0 2 0
  0 1 2 | 0 0 0 2 1 | * * * * 5 * | 0 0 1 1
  0 0 5 | 0 0 0 0 5 | * * * * * 1 | 0 1 0 1
--------+-----------+-------------+--------
♦ 5 1 0 | 5 5 0 0 0 | 1 5 0 0 0 0 | 1 * * *
♦ 5 0 5 | 5 0 5 0 5 | 1 0 5 0 0 1 | * 1 * *
♦ 2 1 2 | 1 2 2 2 1 | 0 1 1 2 1 0 | * * 5 *
♦ 0 1 5 | 0 0 0 5 5 | 0 0 0 0 5 1 | * * * 1