Acronym pappy
Name pentagon-antiprismatical pyramid
Segmentochoron display
Circumradius (1+sqrt(5))/2 = 1.618034
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {3} between tet and tet:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {5} between pap and peppy:   36°
  • at {3} between pap and tet:   arccos(sqrt[7+3 sqrt(5)]/4) = 22.238756°
  • at {3} between peppy and tet:   arccos(sqrt[7+3 sqrt(5)]/4) = 22.238756°
Confer
more general:
n-appy  
segmentochora:
peppypy   ikepy  
general polytopal classes:
segmentochora  

Incidence matrix according to Dynkin symbol

pt || pap   → height = (sqrt(5)-1)/4 = 0.309017

1  *  10  0  0 | 10 10 0  0 | 2 10 0
* 10 |  1  2  2 |  2  2 1  3 | 1  3 1
-----+----------+------------+-------
1  1 | 10  *  * |  2  2 0  0 | 1  3 0
0  2 |  * 10  * |  1  0 1  1 | 1  1 1
0  2 |  *  * 10 |  0  1 0  2 | 0  2 1
-----+----------+------------+-------
1  2 |  2  1  0 | 10  * *  * | 1  1 0
1  2 |  2  0  1 |  * 10 *  * | 0  2 0
0  5 |  0  5  0 |  *  * 2  * | 1  0 1  {5}
0  3 |  0  1  2 |  *  * * 10 | 0  1 1
-----+----------+------------+-------
1  5 |  5  5  0 |  5  0 1  0 | 2  * *  peppy
1  3 |  3  1  2 |  1  2 0  1 | * 10 *  tet
0 10 |  0 10 10 |  0  0 2 10 | *  * 1  pap

{5} || gyro peppy   → height = 1/2

5 * * | 2 1  2 0 0 | 1 2 2  2 1 0 0 | 1 1 2 1 0
* 1 *  0 5  0 5 0 | 0 5 0 10 0 5 0 | 1 0 5 5 1
* * 5 | 0 0  2 1 2 | 0 0 1  2 2 2 1 | 0 1 1 2 1
------+------------+----------------+----------
2 0 0 | 5 *  * * * | 1 1 1  0 0 0 0 | 1 1 1 0 0
1 1 0 | * 5  * * * | 0 2 0  2 0 0 0 | 1 0 2 1 0
1 0 1 | * * 10 * * | 0 0 1  1 1 0 0 | 0 1 1 1 0
0 1 1 | * *  * 5 * | 0 0 0  2 0 2 0 | 0 0 1 2 1
0 0 2 | * *  * * 5 | 0 0 0  0 1 1 1 | 0 1 0 1 1
------+------------+----------------+----------
5 0 0 | 5 0  0 0 0 | 1 * *  * * * * | 1 1 0 0 0
2 1 0 | 1 2  0 0 0 | * 5 *  * * * * | 1 0 1 0 0
2 0 1 | 1 0  2 0 0 | * * 5  * * * * | 0 1 1 0 0
1 1 1 | 0 1  1 1 0 | * * * 10 * * * | 0 0 1 1 0
1 0 2 | 0 0  2 0 1 | * * *  * 5 * * | 0 1 0 1 0
0 1 2 | 0 0  0 2 1 | * * *  * * 5 * | 0 0 0 1 1
0 0 5 | 0 0  0 0 5 | * * *  * * * 1 | 0 1 0 0 1
------+------------+----------------+----------
5 1 0 | 5 5  0 0 0 | 1 5 0  0 0 0 0 | 1 * * * *  peppy
5 0 5 | 5 0 10 0 5 | 1 0 5  0 5 0 1 | * 1 * * *  pap
2 1 1 | 1 2  2 1 0 | 0 1 1  2 0 0 0 | * * 5 * *  tet
1 1 2 | 0 1  2 2 1 | 0 0 0  2 1 1 0 | * * * 5 *  tet
0 1 5 | 0 0  0 5 5 | 0 0 0  0 0 5 1 | * * * * 1  peppy

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