Acronym pepuf, K-4.165 Name pentagonal pucofastegium,pentagon - decagon-prismatic wedge,pentagonal magnabicupolaic ring,{5} || dip,{10} || pecu,{5}-first cap of srahi Segmentochoron display Circumradius sqrt(23+10 sqrt(5)) = 6.735034 Lace cityin approx. ASCII-art ``` x5o x5x x5x ``` Dihedral angles at {3} between squippy and trip:   arccos(-sqrt[9+3 sqrt(5)]/4) = 172.238756° at {4} between pecu and trip:   arccos(-sqrt[(3+sqrt(5))/6]) = 159.094843° at {3} between pecu and squippy:   arccos(-sqrt[7+3 sqrt(5)]/4) = 157.761244° at {5} between pecu and pecu:   144° at {10} between dip and pecu:   18° at {4} between dip and squippy:   arccos(sqrt[(5+2 sqrt(5))/10]) = 13.282526° at {4} between dip and trip:   arccos(sqrt[(10+2 sqrt(5))/15]) = 10.812317° Confer segmentochora family: {n} || 2n-p   uniform relative: srahi   general polytopal classes: segmentochora

Incidence matrix according to Dynkin symbol

```xxx5oxx&#x   → height(1,2) = height(1,3) = sqrt((5-sqrt(5))/10) = 0.525731
height(2,3) = 1

o..5o..    | 5  *  * | 2  2  2 0 0  0 0 0 | 1 2 1 2 1  2 0 0 0 0 | 1 1 2 1 0
.o.5.o.    | * 10  * | 0  1  0 1 1  1 0 0 | 0 1 1 0 0  1 1 1 1 0 | 1 0 1 1 1
..o5..o    | *  * 10 | 0  0  1 0 0  1 1 1 | 0 0 0 1 1  1 0 1 1 1 | 0 1 1 1 1
-----------+---------+--------------------+----------------------+----------
x.. ...    | 2  0  0 | 5  *  * * *  * * * | 1 1 0 1 0  0 0 0 0 0 | 1 1 1 0 0
oo.5oo.&#x | 1  1  0 | * 10  * * *  * * * | 0 1 1 0 0  1 0 0 0 0 | 1 0 1 1 0
o.o5o.o&#x | 1  0  1 | *  * 10 * *  * * * | 0 0 0 1 1  1 0 0 0 0 | 0 1 1 1 0
.x. ...    | 0  2  0 | *  *  * 5 *  * * * | 0 1 0 0 0  0 1 1 0 0 | 1 0 1 0 1
... .x.    | 0  2  0 | *  *  * * 5  * * * | 0 0 1 0 0  0 1 0 1 0 | 1 0 0 1 1
.oo5.oo&#x | 0  1  1 | *  *  * * * 10 * * | 0 0 0 0 0  1 0 1 1 0 | 0 0 1 1 1
..x ...    | 0  0  2 | *  *  * * *  * 5 * | 0 0 0 1 0  0 0 1 0 1 | 0 1 1 0 1
... ..x    | 0  0  2 | *  *  * * *  * * 5 | 0 0 0 0 1  0 0 0 1 1 | 0 1 0 1 1
-----------+---------+--------------------+----------------------+----------
x..5o..    | 5  0  0 | 5  0  0 0 0  0 0 0 | 1 * * * *  * * * * * | 1 1 0 0 0
xx. ...&#x | 2  2  0 | 1  2  0 1 0  0 0 0 | * 5 * * *  * * * * * | 1 0 1 0 0
... ox.&#x | 1  2  0 | 0  2  0 0 1  0 0 0 | * * 5 * *  * * * * * | 1 0 0 1 0
x.x ...&#x | 2  0  2 | 1  0  2 0 0  0 1 0 | * * * 5 *  * * * * * | 0 1 1 0 0
... o.x&#x | 1  0  2 | 0  0  2 0 0  0 0 1 | * * * * 5  * * * * * | 0 1 0 1 0
ooo5ooo&#x | 1  1  1 | 0  1  1 0 0  1 0 0 | * * * * * 10 * * * * | 0 0 1 1 0
.x.5.x.    | 0 10  0 | 0  0  0 5 5  0 0 0 | * * * * *  * 1 * * * | 1 0 0 0 1
.xx ...&#x | 0  2  2 | 0  0  0 1 0  2 1 0 | * * * * *  * * 5 * * | 0 0 1 0 1
... .xx&#x | 0  2  2 | 0  0  0 0 1  2 0 1 | * * * * *  * * * 5 * | 0 0 0 1 1
..x5..x    | 0  0 10 | 0  0  0 0 0  0 5 5 | * * * * *  * * * * 1 | 0 1 0 0 1
-----------+---------+--------------------+----------------------+----------
xx.5ox.&#x ♦ 5 10  0 | 5 10  0 5 5  0 0 0 | 1 5 5 0 0  0 1 0 0 0 | 1 * * * *
x.x5o.x&#x ♦ 5  0 10 | 5  0 10 0 0  0 5 5 | 1 0 0 5 5  0 0 0 0 1 | * 1 * * *
xxx ...&#x ♦ 2  2  2 | 1  2  2 1 0  2 1 0 | 0 1 0 1 0  2 0 1 0 0 | * * 5 * *
... oxx&#x ♦ 1  2  2 | 0  2  2 0 1  2 0 1 | 0 0 1 0 1  2 0 0 1 0 | * * * 5 *
.xx5.xx&#x ♦ 0 10 10 | 0  0  0 5 5 10 5 5 | 0 0 0 0 0  0 1 5 5 1 | * * * * 1
```

```{5} || dip   → height = sqrt((5-2 sqrt(5))/20) = 0.162460

5  * | 2  4  0  0  0 | 1  4  2  2 0 0 0 | 2 2 1 0
* 20 | 0  1  1  1  1 | 0  1  1  1 1 1 1 | 1 1 1 1
-------+---------------+------------------+--------
2  0 | 5  *  *  *  * | 1  2  0  0 0 0 0 | 2 1 0 0
1  1 | * 20  *  *  * | 0  1  1  1 0 0 0 | 1 1 1 0
0  2 | *  * 10  *  * | 0  1  0  0 1 1 0 | 1 1 0 1
0  2 | *  *  * 10  * | 0  0  1  0 1 0 1 | 1 0 1 1
0  2 | *  *  *  * 10 | 0  0  0  1 0 1 1 | 0 1 1 1
-------+---------------+------------------+--------
5  0 | 5  0  0  0  0 | 1  *  *  * * * * | 2 0 0 0
2  2 | 1  2  1  0  0 | * 10  *  * * * * | 1 1 0 0
1  2 | 0  2  0  1  0 | *  * 10  * * * * | 1 0 1 0
1  2 | 0  2  0  0  1 | *  *  * 10 * * * | 0 1 1 0
0 10 | 0  0  5  5  0 | *  *  *  * 2 * * | 1 0 0 1
0  4 | 0  0  2  0  2 | *  *  *  * * 5 * | 0 1 0 1
0  4 | 0  0  0  2  2 | *  *  *  * * * 5 | 0 0 1 1
-------+---------------+------------------+--------
♦ 5 10 | 5 10  5  5  0 | 1  5  5  0 1 0 0 | 2 * * *
♦ 2  4 | 1  4  2  0  2 | 0  2  0  2 0 1 0 | * 5 * *
♦ 1  4 | 0  4  0  2  2 | 0  0  2  2 0 0 1 | * * 5 *
♦ 0 20 | 0  0 10 10 10 | 0  0  0  0 2 5 5 | * * * 1
```

```{10} || pecu   → height = (sqrt(5)-1)/4 = 0.309017

10 *  * | 1 1  1  1 0  0 0 0 | 1 1 1 1 1  1 0 0 0 0 | 1 1 1 1 0
* 5  * | 0 0  2  0 2  2 0 0 | 0 2 1 0 0  2 1 2 1 0 | 1 0 2 1 1
* * 10 | 0 0  0  1 0  1 1 1 | 0 0 0 1 1  1 0 1 1 1 | 0 1 1 1 1
----------+--------------------+----------------------+----------
2 0  0 | 5 *  *  * *  * * * | 1 1 0 1 0  0 0 0 0 0 | 1 1 1 0 0
2 0  0 | * 5  *  * *  * * * | 1 0 1 0 1  0 0 0 0 0 | 1 1 0 1 0
1 1  0 | * * 10  * *  * * * | 0 1 1 0 0  1 0 0 0 0 | 1 0 1 1 0
1 0  1 | * *  * 10 *  * * * | 0 0 0 1 1  1 0 0 0 0 | 0 1 1 1 0
0 2  0 | * *  *  * 5  * * * | 0 1 0 0 0  0 1 1 0 0 | 1 0 1 0 1
0 1  1 | * *  *  * * 10 * * | 0 0 0 0 0  1 0 1 1 0 | 0 0 1 1 1
0 0  2 | * *  *  * *  * 5 * | 0 0 0 1 0  0 0 1 0 1 | 0 1 1 0 1
0 0  2 | * *  *  * *  * * 5 | 0 0 0 0 1  0 0 0 1 1 | 0 1 0 1 1
----------+--------------------+----------------------+----------
10 0  0 | 5 5  0  0 0  0 0 0 | 1 * * * *  * * * * * | 1 1 0 0 0
2 2  0 | 1 0  2  0 1  0 0 0 | * 5 * * *  * * * * * | 1 0 1 0 0
2 1  0 | 0 1  2  0 0  0 0 0 | * * 5 * *  * * * * * | 1 0 0 1 0
2 0  2 | 1 0  0  2 0  0 1 0 | * * * 5 *  * * * * * | 0 1 1 0 0
2 0  2 | 0 1  0  2 0  0 0 1 | * * * * 5  * * * * * | 0 1 0 1 0
1 1  1 | 0 0  1  1 0  1 0 0 | * * * * * 10 * * * * | 0 0 1 1 0
0 5  0 | 0 0  0  0 5  0 0 0 | * * * * *  * 1 * * * | 1 0 0 0 1
0 2  2 | 0 0  0  0 1  2 1 0 | * * * * *  * * 5 * * | 0 0 1 0 1
0 1  2 | 0 0  0  0 0  2 0 1 | * * * * *  * * * 5 * | 0 0 0 1 1
0 0 10 | 0 0  0  0 0  0 5 5 | * * * * *  * * * * 1 | 0 1 0 0 1
----------+--------------------+----------------------+----------
♦ 10 5  0 | 5 5 10  0 5  0 0 0 | 1 5 5 0 0  0 1 0 0 0 | 1 * * * *
♦ 10 0 10 | 5 5  0 10 0  0 5 5 | 1 0 0 5 5  0 0 0 0 1 | * 1 * * *
♦  2 2  2 | 1 0  2  2 1  2 1 0 | 0 1 0 1 0  2 0 1 0 0 | * * 5 * *
♦  2 1  2 | 0 1  2  2 0  2 0 1 | 0 0 1 0 1  2 0 0 1 0 | * * * 5 *
♦  0 5 10 | 0 0  0  0 5 10 5 5 | 0 0 0 0 0  0 1 5 5 1 | * * * * 1
```