Acronym pecuf, K-4.154 Name pentagonal cupofastegium,decagon - pentagon-prismatic wedge,pentagonal orthobicupolaic ring,{10} || pip,{5} || pecu,2/5-luna of stawros Segmentochoron display Circumradius 3+sqrt(5) = 5.236068 Lace cityin approx. ASCII-art ```x5o x5o x5x ``` Dihedral angles at {3} between tet and trip:   arccos(-sqrt[9+3 sqrt(5)]/4) = 172.238756° at {4} between pip and trip:   arccos(-sqrt[(10+2 sqrt(5))/15]) = 169.187683° at {10} between pecu and pecu:   144° at {3} between pecu and tet:   arccos(sqrt[7+3 sqrt(5)]/4) = 22.238756° at {4} between pecu and trip:   arccos(sqrt[(3+sqrt(5))/6]) = 20.905157° at {5} between pip and pecu:   18° Confer segmentochora family: {2n} || n-p   uniform relative: sidpixhi   biform relative: stawros   general polytopal classes: luna   segmentochora

Incidence matrix according to Dynkin symbol

```xx5ox xo&#x   → height = sqrt[(5-2 sqrt(5))/20] = 0.162460
(pip || {10})

o.5o. o.    | 10  * |  2 1  2 0 0 | 1 2  2  1  2 0 | 1 1 2 1
.o5.o .o    |  * 10 |  0 0  2 1 1 | 0 0  2  2  1 1 | 0 2 1 1
------------+-------+-------------+----------------+--------
x. .. ..    |  2  0 | 10 *  * * * | 1 1  1  0  0 0 | 1 1 1 0
.. .. x.    |  2  0 |  * 5  * * * | 0 2  0  0  2 0 | 1 0 2 1
oo5oo oo&#x |  1  1 |  * * 20 * * | 0 0  1  1  1 0 | 0 1 1 1
.x .. ..    |  0  2 |  * *  * 5 * | 0 0  2  0  0 1 | 0 2 1 0
.. .x ..    |  0  2 |  * *  * * 5 | 0 0  0  2  0 1 | 0 2 0 1
------------+-------+-------------+----------------+--------
x.5o. ..    |  5  0 |  5 0  0 0 0 | 2 *  *  *  * * | 1 1 0 0
x. .. x.    |  4  0 |  2 2  0 0 0 | * 5  *  *  * * | 1 0 1 0
xx .. ..&#x |  2  2 |  1 0  2 1 0 | * * 10  *  * * | 0 1 1 0
.. ox ..&#x |  1  2 |  0 0  2 0 1 | * *  * 10  * * | 0 1 0 1
.. .. xo&#x |  2  1 |  0 1  2 0 0 | * *  *  * 10 * | 0 0 1 1
.x5.x ..    |  0 10 |  0 0  0 5 5 | * *  *  *  * 1 | 0 2 0 0
------------+-------+-------------+----------------+--------
x.5o. x.    ♦ 10  0 | 10 5  0 0 0 | 2 5  0  0  0 0 | 1 * * *
xx5ox ..&#x ♦  5 10 |  5 0 10 5 5 | 1 0  5  5  0 1 | * 2 * *
xx .. xo&#x ♦  4  2 |  2 2  4 1 0 | 0 1  2  0  2 0 | * * 5 *
.. ox xo&#x ♦  2  2 |  0 1  4 0 1 | 0 0  0  2  2 0 | * * * 5
```

```xxx5oxo&#x   → height(1,2) = height(2,3) = sqrt((5-sqrt(5))/10) = 0.525731
height(1,3) = 1

o..5o..    | 5  * * | 2  2 1 0 0  0 0 | 1 2 1 2  2 0 0 0 0 | 1 1 2 1 0
.o.5.o.    | * 10 * | 0  1 0 1 1  1 0 | 0 1 1 0  1 1 1 1 0 | 1 0 1 1 1
..o5..o    | *  * 5 | 0  0 1 0 0  2 2 | 0 0 0 2  2 0 2 1 1 | 0 1 2 1 1
-----------+--------+-----------------+--------------------+----------
x.. ...    | 2  0 0 | 5  * * * *  * * | 1 1 0 1  0 0 0 0 0 | 1 1 1 0 0
oo.5oo.&#x | 1  1 0 | * 10 * * *  * * | 0 1 1 0  1 0 0 0 0 | 1 0 1 1 0
o.o5o.o&#x | 1  0 1 | *  * 5 * *  * * | 0 0 0 2  2 0 0 0 0 | 0 1 2 1 0
.x. ...    | 0  2 0 | *  * * 5 *  * * | 0 1 0 0  0 1 1 0 0 | 1 0 1 0 1
... .x.    | 0  2 0 | *  * * * 5  * * | 0 0 1 0  0 1 0 1 0 | 1 0 0 1 1
.oo5.oo    | 0  1 1 | *  * * * * 10 * | 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 1 0 1 | 0 1 1 0 1
-----------+--------+-----------------+--------------------+----------
x..5o..    | 5  0 0 | 5  0 0 0 0  0 0 | 1 * * *  * * * * * | 1 1 0 0 0
xx. ...&#x | 2  2 0 | 1  2 0 1 0  0 0 | * 5 * *  * * * * * | 1 0 1 0 0
... ox.&#x | 1  2 0 | 0  2 0 0 1  0 0 | * * 5 *  * * * * * | 1 0 0 1 0
x.x ...&#x | 2  0 2 | 1  0 2 0 0  0 1 | * * * 5  * * * * * | 0 1 1 0 0
ooo5ooo&#x | 1  1 1 | 0  1 1 0 0  1 0 | * * * * 10 * * * * | 0 0 1 1 0
.x.5.x.    | 0 10 0 | 0  0 0 5 5  0 0 | * * * *  * 1 * * * | 1 0 0 0 1
.xx ...&#x | 0  2 2 | 0  0 0 1 0  2 1 | * * * *  * * 5 * * | 0 0 1 0 1
... .xo&#x | 0  2 1 | 0  0 0 0 1  2 0 | * * * *  * * * 5 * | 0 0 0 1 1
..x5..o    | 0  0 5 | 0  0 0 0 0  0 5 | * * * *  * * * * 1 | 0 1 0 0 1
-----------+--------+-----------------+--------------------+----------
xx.5ox.&#x ♦ 5 10 0 | 5 10 0 5 5  0 0 | 1 5 5 0  0 1 0 0 0 | 1 * * * *
x.x5o.o&#x ♦ 5  0 5 | 5  0 5 0 0  0 5 | 1 0 0 5  0 0 0 0 1 | * 1 * * *
xxx ...&#x ♦ 2  2 2 | 1  2 2 1 0  2 1 | 0 1 0 1  2 0 1 0 0 | * * 5 * *
... oxo&#x ♦ 1  2 1 | 0  2 1 0 1  2 0 | 0 0 1 0  2 0 0 1 0 | * * * 5 *
.xx5.oo&#x ♦ 0 10 5 | 0  0 0 5 5 10 5 | 0 0 0 0  0 1 5 5 1 | * * * * 1
```
```or
o..5o..     & | 10  * |  2  2 1 0 0 | 1  2  1 2  2 0 | 1 1 2 1
.o.5.o.       |  * 10 |  0  2 0 1 1 | 0  2  2 0  1 1 | 2 0 1 1
--------------+-------+-------------+----------------+--------
x.. ...     & |  2  0 | 10  * * * * | 1  1  0 1  0 0 | 1 1 1 0
oo.5oo.&#x  & |  1  1 |  * 20 * * * | 0  1  1 0  1 0 | 1 0 1 1
o.o5o.o&#x    |  2  0 |  *  * 5 * * | 0  0  0 2  2 0 | 0 1 2 1
.x. ...       |  0  2 |  *  * * 5 * | 0  2  0 0  0 1 | 2 0 1 0
... .x.       |  0  2 |  *  * * * 5 | 0  0  2 0  0 1 | 2 0 0 1
--------------+-------+-------------+----------------+--------
x..5o..     & |  5  0 |  5  0 0 0 0 | 2  *  * *  * * | 1 1 0 0
xx. ...&#x  & |  2  2 |  1  2 0 1 0 | * 10  * *  * * | 1 0 1 0
... ox.&#x  & |  1  2 |  0  2 0 0 1 | *  * 10 *  * * | 1 0 0 1
x.x ...&#x    |  4  0 |  2  0 2 0 0 | *  *  * 5  * * | 0 1 1 0
ooo5ooo&#x    |  2  1 |  0  2 1 0 0 | *  *  * * 10 * | 0 0 1 1
.x.5.x.       |  0 10 |  0  0 0 5 5 | *  *  * *  * 1 | 2 0 0 0
--------------+-------+-------------+----------------+--------
xx.5ox.&#x  & ♦  5 10 |  5 10 0 5 5 | 1  5  5 0  0 1 | 2 * * *
x.x5o.o&#x    ♦ 10  0 | 10  0 5 0 0 | 2  0  0 5  0 0 | * 1 * *
xxx ...&#x    ♦  4  2 |  2  4 2 1 0 | 0  2  0 1  2 0 | * * 5 *
... oxo&#x    ♦  2  2 |  0  4 1 0 1 | 0  0  2 0  2 0 | * * * 5
```

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

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