Acronym padedip Name pentagon - decagon duoprism Circumradius sqrt[(10+3 sqrt(5))/5] = 1.828016 Volume 25[2+sqrt(5)]/8 = 13.237712 General of army (is itself convex) Colonel of regiment (is itself locally convex) Dihedral angles at {5} between pip and pip:   144° at {10} between dip and dip:   108° at {4} between dip and pip:   90° Confer general duoprisms: n,m-dip   2n,m-dip   5,n-dip   10,n-dip   general polytopal classes: bistratic lace towers Externallinks

Incidence matrix according to Dynkin symbol

```x5o x10o

. . .  . | 50 |  2  2 |  1  4 1 |  2 2
---------+----+-------+---------+-----
x . .  . |  2 | 50  * |  1  2 0 |  2 1
. . x  . |  2 |  * 50 |  0  2 1 |  1 2
---------+----+-------+---------+-----
x5o .  . |  5 |  5  0 | 10  * * |  2 0
x . x  . |  4 |  2  2 |  * 50 * |  1 1
. . x10o | 10 |  0 10 |  *  * 5 |  0 2
---------+----+-------+---------+-----
x5o x  . ♦ 10 | 10  5 |  2  5 0 | 10 *
x . x10o ♦ 20 | 10 20 |  0 10 2 |  * 5
```

```x5o x5x

. . . . | 50 |  2  1  1 |  1  2  2 1 | 1 1 2
--------+----+----------+------------+------
x . . . |  2 | 50  *  * |  1  1  1 0 | 1 1 1
. . x . |  2 |  * 25  * |  0  2  0 1 | 1 0 2
. . . x |  2 |  *  * 25 |  0  0  2 1 | 0 1 2
--------+----+----------+------------+------
x5o . . |  5 |  5  0  0 | 10  *  * * | 1 1 0
x . x . |  4 |  2  2  0 |  * 25  * * | 1 0 1
x . . x |  4 |  2  0  2 |  *  * 25 * | 0 1 1
. . x5x | 10 |  0  5  5 |  *  *  * 5 | 0 0 2
--------+----+----------+------------+------
x5o x . ♦ 10 | 10  5  0 |  2  5  0 0 | 5 * *
x5o . x ♦ 10 | 10  0  5 |  2  0  5 0 | * 5 *
x . x5x ♦ 20 | 10 10 10 |  0  5  5 2 | * * 5
```

```ofx xxx10ooo&#xt   → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785
height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057
({10} || pseudo (f,x)-dip || dip)

o.. o..10o..     | 10  *  * |  2  2  0  0  0  0 | 1  1  4 0  0  0 0 |  2 2 0 0
.o. .o.10.o.     |  * 20  * |  0  1  2  1  0  0 | 0  1  2 1  2  0 0 |  2 1 1 0
..o ..o10..o     |  *  * 20 |  0  0  0  1  1  2 | 0  1  0 0  2  2 1 |  2 0 1 1
-----------------+----------+-------------------+-------------------+---------
... x..  ...     |  2  0  0 | 10  *  *  *  *  * | 1  0  2 0  0  0 0 |  1 2 0 0
oo. oo.10oo.&#x  |  1  1  0 |  * 20  *  *  *  * | 0  1  2 0  0  0 0 |  2 1 0 0
... .x.  ...     |  0  2  0 |  *  * 20  *  *  * | 0  0  1 1  1  0 0 |  1 1 1 0
.oo .oo10.oo&#x  |  0  1  1 |  *  *  * 20  *  * | 0  1  0 0  2  0 0 |  2 0 1 0
..x ...  ...     |  0  0  2 |  *  *  *  * 10  * | 0  1  0 0  0  2 0 |  2 0 0 1
... ..x  ...     |  0  0  2 |  *  *  *  *  * 20 | 0  0  0 0  1  1 1 |  1 0 1 1
-----------------+----------+-------------------+-------------------+---------
... x..10o..     | 10  0  0 | 10  0  0  0  0  0 | 1  *  * *  *  * * |  0 2 0 0
ofx ...  ...&#xt |  1  2  2 |  0  2  0  2  1  0 | * 10  * *  *  * * |  2 0 0 0
... xx.  ...&#x  |  2  2  0 |  1  2  1  0  0  0 | *  * 20 *  *  * * |  1 1 0 0
... .x.10.o.     |  0 10  0 |  0  0 10  0  0  0 | *  *  * 2  *  * * |  0 1 1 0
... .xx  ...&#x  |  0  2  2 |  0  0  1  2  0  1 | *  *  * * 20  * * |  1 0 1 0
..x ..x  ...     |  0  0  4 |  0  0  0  0  2  2 | *  *  * *  * 10 * |  1 0 0 1
... ..x10..o     |  0  0 10 |  0  0  0  0  0 10 | *  *  * *  *  * 2 |  0 0 1 1
-----------------+----------+-------------------+-------------------+---------
ofx xxx  ...&#xt ♦  2  4  4 |  1  4  2  4  2  2 | 0  2  2 0  2  1 0 | 10 * * *
... xx.10oo.&#x  ♦ 10 10  0 | 10 10 10  0  0  0 | 1  0 10 1  0  0 0 |  * 2 * *
... .xx10.oo&#x  ♦  0 10 10 |  0  0 10 10  0 10 | 0  0  0 1 10  0 1 |  * * 2 *
..x ..x10..o     ♦  0  0 20 |  0  0  0  0 10 20 | 0  0  0 0  0 10 2 |  * * * 1
```

```ofx xxx5xxx&#xt   → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785
height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057
({10} || pseudo (f,x)-dip || dip)

o.. o..5o..     | 10  *  * | 1 1  2  0  0  0  0  0  0 | 1  1  2  2 0  0  0 0 0 0 | 1 1 2 0 0
.o. .o.5.o.     |  * 20  * | 0 0  1  1  1  1  0  0  0 | 0  1  1  1 1  1  1 0 0 0 | 1 1 1 1 0
..o ..o5..o     |  *  * 20 | 0 0  0  0  0  1  1  1  1 | 0  1  0  0 0  1  1 1 1 1 | 1 1 0 1 1
----------------+----------+--------------------------+--------------------------+----------
... x.. ...     |  2  0  0 | 5 *  *  *  *  *  *  *  * | 1  0  2  0 0  0  0 0 0 0 | 1 0 2 0 0
... ... x..     |  2  0  0 | * 5  *  *  *  *  *  *  * | 1  0  0  2 0  0  0 0 0 0 | 0 1 2 0 0
oo. oo.5oo.&#x  |  1  1  0 | * * 20  *  *  *  *  *  * | 0  1  1  1 0  0  0 0 0 0 | 1 1 1 0 0
... .x. ...     |  0  2  0 | * *  * 10  *  *  *  *  * | 0  0  1  0 1  1  0 0 0 0 | 1 0 1 1 0
... ... .x.     |  0  2  0 | * *  *  * 10  *  *  *  * | 0  0  0  1 1  0  1 0 0 0 | 0 1 1 1 0
.oo .oo5.oo&#x  |  0  1  1 | * *  *  *  * 20  *  *  * | 0  1  0  0 0  1  1 0 0 0 | 1 1 0 1 0
..x ... ...     |  0  0  2 | * *  *  *  *  * 10  *  * | 0  1  0  0 0  0  0 1 1 0 | 1 1 0 0 1
... ..x ...     |  0  0  2 | * *  *  *  *  *  * 10  * | 0  0  0  0 0  1  0 1 0 1 | 1 0 0 1 1
... ... ..x     |  0  0  2 | * *  *  *  *  *  *  * 10 | 0  0  0  0 0  0  1 0 1 1 | 0 1 0 1 1
----------------+----------+--------------------------+--------------------------+----------
... x..5x..     | 10  0  0 | 5 5  0  0  0  0  0  0  0 | 1  *  *  * *  *  * * * * | 0 0 2 0 0
ofx ... ...&#xt |  1  2  2 | 0 0  2  0  0  2  1  0  0 | * 10  *  * *  *  * * * * | 1 1 0 0 0
... xx. ...&#x  |  2  2  0 | 1 0  2  1  0  0  0  0  0 | *  * 10  * *  *  * * * * | 1 0 1 0 0
... ... xx.&#x  |  2  2  0 | 0 1  2  0  1  0  0  0  0 | *  *  * 10 *  *  * * * * | 0 1 1 0 0
... .x.5.x.     |  0 10  0 | 0 0  0  5  5  0  0  0  0 | *  *  *  * 2  *  * * * * | 0 0 1 1 0
... .xx ...&#x  |  0  2  2 | 0 0  0  1  0  2  0  1  0 | *  *  *  * * 10  * * * * | 1 0 0 1 0
... ... .xx&#x  |  0  2  2 | 0 0  0  0  1  2  0  0  1 | *  *  *  * *  * 10 * * * | 0 1 0 1 0
..x ..x ...     |  0  0  4 | 0 0  0  0  0  0  2  2  0 | *  *  *  * *  *  * 5 * * | 1 0 0 0 1
..x ... ..x     |  0  0  4 | 0 0  0  0  0  0  2  0  2 | *  *  *  * *  *  * * 5 * | 0 1 0 0 1
... ..x5..x     |  0  0 10 | 0 0  0  0  0  0  0  5  5 | *  *  *  * *  *  * * * 2 | 0 0 0 1 1
----------------+----------+--------------------------+--------------------------+----------
ofx xxx ...&#xt ♦  2  4  4 | 1 0  4  2  0  4  2  2  0 | 0  2  2  0 0  2  0 1 0 0 | 5 * * * *
ofx ... xxx&#xt ♦  2  4  4 | 0 1  4  0  2  4  2  0  2 | 0  2  0  2 0  0  2 0 1 0 | * 5 * * *
... xx.5xx.&#x  ♦ 10 10  0 | 5 5 10  5  5  0  0  0  0 | 1  0  5  5 1  0  0 0 0 0 | * * 2 * *
... .xx5.xx&#x  ♦  0 10 10 | 0 0  0  5  5 10  0  5  5 | 0  0  0  0 1  5  5 0 0 1 | * * * 2 *
..x ..x5..x     ♦  0  0 20 | 0 0  0  0  0  0 10 10 10 | 0  0  0  0 0  0  0 5 5 2 | * * * * 1
```