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°
Confer
general pyramids:
pt || n-p  
uniform relative:
rox  
general polytopal classes:
segmentochora  

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

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