Acronym peppyp, K-4.38 Name pentagon-pyramidal prism,J2 prism,line || pip Segmentochoron display Circumradius sqrt[(7+sqrt(5))/8] = 1.074481 Dihedral angles at {4} between trip and trip:   arccos(-sqrt(5)/3) = 138.189685° at {5} between peppy and pip:   90° at {3} between peppy and trip:   90° at {4} between pip and trip:   arccos(sqrt[(5+2 sqrt(5))/15]) = 37.377368° Confer general pyramid-prisms: n-pyp   uniform relative: ipe   general polytopal classes: segmentochora Externallinks

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

Incidence matrix according to Dynkin symbol

```xx ox5oo&#x   → height = sqrt((5-sqrt(5))/10) = 0.525731
(line || pip)

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

```peppy || peppy   → height = 1

1 * * * | 5 1 0 0 0 0 | 5 5 0 0 0 0 | 1 5 0 0  top-tip
* 5 * * | 1 0 2 1 0 0 | 2 1 1 0 0 0 | 1 2 1 0  top-base
* * 1 * | 0 1 0 0 5 0 | 0 5 0 0 5 0 | 0 5 0 1  bottom-tip
* * * 5 | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1  bottom-base
----------+-------------+-------------+--------
1 1 0 0 | 5 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
1 0 1 0 | * 1 * * * * | 0 5 0 0 0 0 | 0 5 0 0
0 2 0 0 | * * 5 * * * | 1 0 1 1 0 0 | 1 1 1 0
0 1 0 1 | * * * 5 * * | 0 1 0 2 0 0 | 0 2 1 0
0 0 1 1 | * * * * 5 * | 0 1 0 0 2 0 | 0 2 0 1
0 0 0 2 | * * * * * 5 | 0 0 0 1 1 1 | 0 1 1 1
----------+-------------+-------------+--------
1 2 0 0 | 2 0 1 0 0 0 | 5 * * * * * | 1 1 0 0
1 1 1 1 | 1 1 0 1 1 0 | * 5 * * * * | 0 2 0 0
0 5 0 0 | 0 0 5 0 0 0 | * * 1 * * * | 1 0 1 0
0 2 0 2 | 0 0 1 2 0 1 | * * * 5 * * | 0 1 1 0
0 0 1 2 | 0 0 0 0 2 1 | * * * * 5 * | 0 1 0 1
0 0 0 5 | 0 0 0 0 0 5 | * * * * * 1 | 0 0 1 1
----------+-------------+-------------+--------
♦ 1 5 0 0 | 5 0 5 0 0 0 | 5 0 1 0 0 0 | 1 * * *
♦ 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * 5 * *
♦ 0 5 0 5 | 0 0 5 5 0 5 | 0 0 1 5 0 1 | * * 1 *
♦ 0 0 1 5 | 0 0 0 0 5 5 | 0 0 0 0 5 1 | * * * 1
```

```oxxo5oooo&#xr   → height(1,2) = height(3,4) = sqrt((5-sqrt(5))/10) = 0.525731
height(1,4) = height(2,3) = 1
( (pt || {5})  ||  (pt || {5}) )

o...5o...     | 1 * * * | 5 1 0 0 0 0 | 5 5 0 0 0 0 | 1 5 0 0
.o..5.o..     | * 5 * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
..o.5..o.     | * * 5 * | 0 0 0 1 2 1 | 0 1 0 2 1 2 | 0 2 1 1
...o5...o     | * * * 1 | 0 1 0 0 0 5 | 0 5 0 0 0 5 | 0 5 0 1
--------------+---------+-------------+-------------+--------
oo..5oo..&#x  | 1 1 0 0 | 5 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
o..o5o..o&#x  | 1 0 0 1 | * 1 * * * * | 0 5 0 0 0 0 | 0 5 0 0
.x.. ....     | 0 2 0 0 | * * 5 * * * | 1 0 1 1 0 0 | 1 1 1 0
.oo.5.oo.&#x  | 0 1 1 0 | * * * 5 * * | 0 1 0 2 0 0 | 0 2 1 0
..x. ....     | 0 0 2 0 | * * * * 5 * | 0 0 0 1 1 1 | 0 1 1 1
..oo5..oo&#x  | 0 0 1 1 | * * * * * 5 | 0 1 0 0 0 2 | 0 2 0 1
--------------+---------+-------------+-------------+--------
ox.. ....&#x  | 1 2 0 0 | 2 0 1 0 0 0 | 5 * * * * * | 1 1 0 0
oooo5oooo&#xr | 1 1 1 1 | 1 1 0 1 0 1 | * 5 * * * * | 0 2 0 0
.x..5.o..     | 0 5 0 0 | 0 0 5 0 0 0 | * * 1 * * * | 1 0 1 0
.xx. ....&#x  | 0 2 2 0 | 0 0 1 2 1 0 | * * * 5 * * | 0 1 1 0
..x.5..o.     | 0 0 5 0 | 0 0 0 0 5 0 | * * * * 1 * | 0 0 1 1
..xo ....&#x  | 0 0 2 1 | 0 0 0 0 1 2 | * * * * * 5 | 0 1 0 1
--------------+---------+-------------+-------------+--------
ox..5oo..&#x  ♦ 1 5 0 0 | 5 0 5 0 0 0 | 5 0 1 0 0 0 | 1 * * *
oxxo ....&#xr ♦ 1 2 2 1 | 2 1 1 2 1 2 | 1 2 0 1 0 1 | * 5 * *
.xx.5.oo.&#x  ♦ 0 5 5 0 | 0 0 5 5 5 0 | 0 0 1 5 1 0 | * * 1 *
..xo5..oo&#x  ♦ 0 0 5 1 | 0 0 0 0 5 5 | 0 0 0 0 1 5 | * * * 1
```

```o(xo)x5o(oo)o&#xt
(pt || ({5} || pt) || para {5})

o(..).5o(..).     | 1 * * * | 5 1 0 0 0 0 | 5 5 0 0 0 0 | 1 5 0 0
.(o.).5.(o.).     | * 5 * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
.(.o).5.(.o).     | * * 1 * | 0 1 0 0 5 0 | 0 5 0 0 5 0 | 0 5 0 1
.(..)o5.(..)o     | * * * 5 | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1
------------------+---------+-------------+-------------+--------
o(o.).5o(o.).&#x  | 1 1 0 0 | 5 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
o(.o).5o(.o).&#x  | 1 0 1 0 | * 1 * * * * | 0 5 0 0 0 0 | 0 5 0 0
.(x.). .(..).     | 0 2 0 0 | * * 5 * * * | 1 0 1 1 0 0 | 1 1 1 0
.(o.)o5.(o.)o&#x  | 0 1 0 1 | * * * 5 * * | 0 1 0 2 0 0 | 0 2 1 0
.(.o)o5.(.o)o&#x  | 0 0 1 1 | * * * * 5 * | 0 1 0 0 2 0 | 0 2 0 1
.(..)x .(..).     | 0 0 0 2 | * * * * * 5 | 0 0 0 1 1 1 | 0 1 1 1
------------------+---------+-------------+-------------+--------
o(x.). .(..).&#x  | 1 2 0 0 | 2 0 1 0 0 0 | 5 * * * * * | 1 1 0 0
o(oo)o5o(oo)o&#xt | 1 1 1 1 | 1 1 0 1 1 0 | * 5 * * * * | 0 2 0 0
.(x.).5.(o.).     | 0 5 0 0 | 0 0 5 0 0 0 | * * 1 * * * | 1 0 1 0
.(x.)x .(..).&#x  | 0 2 0 2 | 0 0 1 2 0 1 | * * * 5 * * | 0 1 1 0
.(.o)x .(..).&#x  | 0 0 1 2 | 0 0 0 0 2 1 | * * * * 5 * | 0 1 0 1
.(..)x5.(..)o     | 0 0 0 5 | 0 0 0 0 0 5 | * * * * * 1 | 0 0 1 1
------------------+---------+-------------+-------------+--------
o(x.).5o(o.).&#x  ♦ 1 5 0 0 | 5 0 5 0 0 0 | 5 0 1 0 0 0 | 1 * * *
o(xo)x .(..).&#xt ♦ 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * 5 * *
.(x.)x5.(o.)o&#x  ♦ 0 5 0 5 | 0 0 5 5 0 5 | 0 0 1 5 0 1 | * * 1 *
.(.o)x5.(.o)o&#x  ♦ 0 0 1 5 | 0 0 0 0 5 5 | 0 0 0 0 5 1 | * * * 1
```