Acronym iddip, K-4.90 Name icosidodecahedron prism Segmentochoron display Cross sections ` ©` Circumradius sqrt[7+2 sqrt(5)]/2 = 1.693527 General of army (is itself convex) Colonel of regiment (is itself locally convex) Dihedral angles at {4} between pip and trip:   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632° at {5} between id and pip:   90° at {3} between id and trip:   90° Confer related segmentochora: perope   general polytopal classes: segmentochora Externallinks

As abstract polytope iddip is isomorphic to giddip, thereby replacing id by gid and pip by stip.

Incidence matrix according to Dynkin symbol

```x o3x5o

. . . . | 60 |  1   4 |  4  2  2 |  2  2 1
--------+----+--------+----------+--------
x . . . |  2 | 30   * |  4  0  0 |  2  2 0
. . x . |  2 |  * 120 |  1  1  1 |  1  1 1
--------+----+--------+----------+--------
x . x . |  4 |  2   2 | 60  *  * |  1  1 0
. o3x . |  3 |  0   3 |  * 40  * |  1  0 1
. . x5o |  5 |  0   5 |  *  * 24 |  0  1 1
--------+----+--------+----------+--------
x o3x . ♦  6 |  3   6 |  3  2  0 | 20  * *
x . x5o ♦ 10 |  5  10 |  5  0  2 |  * 12 *
. o3x5o ♦ 30 |  0  60 |  0 20 12 |  *  * 2
```

```x o3x5/4o

. . .   . | 60 |  1   4 |  4  2  2 |  2  2 1
----------+----+--------+----------+--------
x . .   . |  2 | 30   * |  4  0  0 |  2  2 0
. . x   . |  2 |  * 120 |  1  1  1 |  1  1 1
----------+----+--------+----------+--------
x . x   . |  4 |  2   2 | 60  *  * |  1  1 0
. o3x   . |  3 |  0   3 |  * 40  * |  1  0 1
. . x5/4o |  5 |  0   5 |  *  * 24 |  0  1 1
----------+----+--------+----------+--------
x o3x   . ♦  6 |  3   6 |  3  2  0 | 20  * *
x . x5/4o ♦ 10 |  5  10 |  5  0  2 |  * 12 *
. o3x5/4o ♦ 30 |  0  60 |  0 20 12 |  *  * 2
```

```x o3/2x5o

. .   . . | 60 |  1   4 |  4  2  2 |  2  2 1
----------+----+--------+----------+--------
x .   . . |  2 | 30   * |  4  0  0 |  2  2 0
. .   x . |  2 |  * 120 |  1  1  1 |  1  1 1
----------+----+--------+----------+--------
x .   x . |  4 |  2   2 | 60  *  * |  1  1 0
. o3/2x . |  3 |  0   3 |  * 40  * |  1  0 1
. .   x5o |  5 |  0   5 |  *  * 24 |  0  1 1
----------+----+--------+----------+--------
x o3/2x . ♦  6 |  3   6 |  3  2  0 | 20  * *
x .   x5o ♦ 10 |  5  10 |  5  0  2 |  * 12 *
. o3/2x5o ♦ 30 |  0  60 |  0 20 12 |  *  * 2
```

```x o3/2x5/4o

. .   .   . | 60 |  1   4 |  4  2  2 |  2  2 1
------------+----+--------+----------+--------
x .   .   . |  2 | 30   * |  4  0  0 |  2  2 0
. .   x   . |  2 |  * 120 |  1  1  1 |  1  1 1
------------+----+--------+----------+--------
x .   x   . |  4 |  2   2 | 60  *  * |  1  1 0
. o3/2x   . |  3 |  0   3 |  * 40  * |  1  0 1
. .   x5/4o |  5 |  0   5 |  *  * 24 |  0  1 1
------------+----+--------+----------+--------
x o3/2x   . ♦  6 |  3   6 |  3  2  0 | 20  * *
x .   x5/4o ♦ 10 |  5  10 |  5  0  2 |  * 12 *
. o3/2x5/4o ♦ 30 |  0  60 |  0 20 12 |  *  * 2
```

```oo3xx5oo&#x   → height = 1
(id || id)

o.3o.5o.    | 30  * |  4  1  0 |  2  2  4  0  0 | 1  2  2 0
.o3.o5.o    |  * 30 |  0  1  4 |  0  0  4  2  2 | 0  2  2 1
------------+-------+----------+----------------+----------
.. x. ..    |  2  0 | 60  *  * |  1  1  1  0  0 | 1  1  1 0
oo3oo5oo&#x |  1  1 |  * 30  * |  0  0  4  0  0 | 0  2  2 0
.. .x ..    |  0  2 |  *  * 60 |  0  0  1  1  1 | 0  1  1 1
------------+-------+----------+----------------+----------
o.3x. ..    |  3  0 |  3  0  0 | 20  *  *  *  * | 1  1  0 0
.. x.5o.    |  5  0 |  5  0  0 |  * 12  *  *  * | 1  0  1 0
.. xx ..&#x |  2  2 |  1  2  1 |  *  * 60  *  * | 0  1  1 0
.o3.x ..    |  0  3 |  0  0  3 |  *  *  * 20  * | 0  1  0 1
.. .x5.o    |  0  5 |  0  0  5 |  *  *  *  * 12 | 0  0  1 1
------------+-------+----------+----------------+----------
o.3x.5o.    ♦ 30  0 | 60  0  0 | 20 12  0  0  0 | 1  *  * *
oo3xx ..&#x ♦  3  3 |  3  3  3 |  1  0  3  1  0 | * 20  * *
.. xx5oo&#x ♦  5  5 |  5  5  5 |  0  1  5  0  1 | *  * 12 *
.o3.x5.o    ♦  0 30 |  0  0 60 |  0  0  0 20 12 | *  *  * 1
```

```xxxxx xoxfo5ofxox&#xt   → outer heights = sqrt[(5-sqrt(5))/10] = 0.525731
inner heights = sqrt[(5+sqrt(5))/10] = 0.850651
(pip || pseudo dual f-pip || pseudo dip || pseudo f-pip || dual pip)

o.... o....5o....     | 10  *  *  *  * | 1  2  2 0  0  0  0  0  0 0  0 0  0 | 2 1  2  2  1  0  0 0 0  0  0  0  0  0 0 0 | 1 2 1 1 0 0 0 0 0
.o... .o...5.o...     |  * 10  *  *  * | 0  0  2 1  2  0  0  0  0 0  0 0  0 | 0 0  2  1  2  2  1 0 0  0  0  0  0  0 0 0 | 0 1 2 1 1 0 0 0 0
..o.. ..o..5..o..     |  *  * 20  *  * | 0  0  0 0  1  1  1  1  1 0  0 0  0 | 0 0  0  0  1  1  1 1 1  1  1  1  0  0 0 0 | 0 0 1 1 1 1 1 0 0
...o. ...o.5...o.     |  *  *  * 10  * | 0  0  0 0  0  0  0  0  2 1  2 0  0 | 0 0  0  0  0  0  0 0 0  2  2  1  2  1 0 0 | 0 0 0 1 0 2 1 1 0
....o ....o5....o     |  *  *  *  * 10 | 0  0  0 0  0  0  0  0  0 0  2 1  2 | 0 0  0  0  0  0  0 0 0  0  1  0  2  2 2 1 | 0 0 0 1 0 1 0 2 1
----------------------+----------------+------------------------------------+-------------------------------------------+------------------
x.... ..... .....     |  2  0  0  0  0 | 5  *  * *  *  *  *  *  * *  * *  * | 2 0  2  0  0  0  0 0 0  0  0  0  0  0 0 0 | 1 2 1 0 0 0 0 0 0
..... x.... .....     |  2  0  0  0  0 | * 10  * *  *  *  *  *  * *  * *  * | 1 1  0  1  0  0  0 0 0  0  0  0  0  0 0 0 | 1 1 0 1 0 0 0 0 0
oo... oo...5oo...&#x  |  1  1  0  0  0 | *  * 20 *  *  *  *  *  * *  * *  * | 0 0  1  1  1  0  0 0 0  0  0  0  0  0 0 0 | 0 1 1 1 0 0 0 0 0
.x... ..... .....     |  0  2  0  0  0 | *  *  * 5  *  *  *  *  * *  * *  * | 0 0  2  0  0  2  0 0 0  0  0  0  0  0 0 0 | 0 1 2 0 1 0 0 0 0
.oo.. .oo..5.oo..&#x  |  0  1  1  0  0 | *  *  * * 20  *  *  *  * *  * *  * | 0 0  0  0  1  1  1 0 0  0  0  0  0  0 0 0 | 0 0 1 1 1 0 0 0 0
..x.. ..... .....     |  0  0  2  0  0 | *  *  * *  * 10  *  *  * *  * *  * | 0 0  0  0  0  1  0 1 1  1  0  0  0  0 0 0 | 0 0 1 0 1 1 1 0 0
..... ..x.. .....     |  0  0  2  0  0 | *  *  * *  *  * 10  *  * *  * *  * | 0 0  0  0  0  0  1 1 0  0  1  0  0  0 0 0 | 0 0 0 1 1 1 0 0 0
..... ..... ..x..     |  0  0  2  0  0 | *  *  * *  *  *  * 10  * *  * *  * | 0 0  0  0  1  0  0 0 1  0  0  1  0  0 0 0 | 0 0 1 1 0 0 1 0 0
..oo. ..oo.5..oo.&#x  |  0  0  1  1  0 | *  *  * *  *  *  *  * 20 *  * *  * | 0 0  0  0  0  0  0 0 0  1  1  1  0  0 0 0 | 0 0 0 1 0 1 1 0 0
...x. ..... .....     |  0  0  0  2  0 | *  *  * *  *  *  *  *  * 5  * *  * | 0 0  0  0  0  0  0 0 0  2  0  0  2  0 0 0 | 0 0 0 0 0 2 1 1 0
...oo ...oo5...oo&#x  |  0  0  0  1  1 | *  *  * *  *  *  *  *  * * 20 *  * | 0 0  0  0  0  0  0 0 0  0  1  0  1  1 0 0 | 0 0 0 1 0 1 0 1 0
....x ..... .....     |  0  0  0  0  2 | *  *  * *  *  *  *  *  * *  * 5  * | 0 0  0  0  0  0  0 0 0  0  0  0  2  0 2 0 | 0 0 0 0 0 1 0 2 1
..... ..... ....x     |  0  0  0  0  2 | *  *  * *  *  *  *  *  * *  * * 10 | 0 0  0  0  0  0  0 0 0  0  0  0  0  1 1 1 | 0 0 0 1 0 0 0 1 1
----------------------+----------------+------------------------------------+-------------------------------------------+------------------
x.... x.... .....     |  4  0  0  0  0 | 2  2  0 0  0  0  0  0  0 0  0 0  0 | 5 *  *  *  *  *  * * *  *  *  *  *  * * * | 1 1 0 0 0 0 0 0 0
..... x....5o....     |  5  0  0  0  0 | 0  5  0 0  0  0  0  0  0 0  0 0  0 | * 2  *  *  *  *  * * *  *  *  *  *  * * * | 1 0 0 1 0 0 0 0 0
xx... ..... .....&#x  |  2  2  0  0  0 | 1  0  2 1  0  0  0  0  0 0  0 0  0 | * * 10  *  *  *  * * *  *  *  *  *  * * * | 0 1 1 0 0 0 0 0 0
..... xo... .....&#x  |  2  1  0  0  0 | 0  1  2 0  0  0  0  0  0 0  0 0  0 | * *  * 10  *  *  * * *  *  *  *  *  * * * | 0 1 0 1 0 0 0 0 0
..... ..... ofx..&#xt |  1  2  2  0  0 | 0  0  2 0  2  0  0  1  0 0  0 0  0 | * *  *  * 10  *  * * *  *  *  *  *  * * * | 0 0 1 1 0 0 0 0 0
.xx.. ..... .....&#x  |  0  2  2  0  0 | 0  0  0 1  2  1  0  0  0 0  0 0  0 | * *  *  *  * 10  * * *  *  *  *  *  * * * | 0 0 1 0 1 0 0 0 0
..... .ox.. .....&#x  |  0  1  2  0  0 | 0  0  0 0  2  0  1  0  0 0  0 0  0 | * *  *  *  *  * 10 * *  *  *  *  *  * * * | 0 0 0 1 1 0 0 0 0
..x.. ..x.. .....     |  0  0  4  0  0 | 0  0  0 0  0  2  2  0  0 0  0 0  0 | * *  *  *  *  *  * 5 *  *  *  *  *  * * * | 0 0 0 0 1 1 0 0 0
..x.. ..... ..x..     |  0  0  4  0  0 | 0  0  0 0  0  2  0  2  0 0  0 0  0 | * *  *  *  *  *  * * 5  *  *  *  *  * * * | 0 0 1 0 0 0 1 0 0
..xx. ..... .....&#x  |  0  0  2  2  0 | 0  0  0 0  0  1  0  0  2 1  0 0  0 | * *  *  *  *  *  * * * 10  *  *  *  * * * | 0 0 0 0 0 1 1 0 0
..... ..xfo .....&#xt |  0  0  2  2  1 | 0  0  0 0  0  0  1  0  2 0  2 0  0 | * *  *  *  *  *  * * *  * 10  *  *  * * * | 0 0 0 1 0 1 0 0 0
..... ..... ..xo.&#x  |  0  0  2  1  0 | 0  0  0 0  0  0  0  1  2 0  0 0  0 | * *  *  *  *  *  * * *  *  * 10  *  * * * | 0 0 0 1 0 0 1 0 0
...xx ..... .....&#x  |  0  0  0  2  2 | 0  0  0 0  0  0  0  0  0 1  2 1  0 | * *  *  *  *  *  * * *  *  *  * 10  * * * | 0 0 0 0 0 1 0 1 0
..... ..... ...ox&#x  |  0  0  0  1  2 | 0  0  0 0  0  0  0  0  0 0  2 0  1 | * *  *  *  *  *  * * *  *  *  *  * 10 * * | 0 0 0 1 0 0 0 1 0
....x ..... ....x     |  0  0  0  0  4 | 0  0  0 0  0  0  0  0  0 0  0 2  2 | * *  *  *  *  *  * * *  *  *  *  *  * 5 * | 0 0 0 0 0 0 0 1 1
..... ....o5....x     |  0  0  0  0  5 | 0  0  0 0  0  0  0  0  0 0  0 0  5 | * *  *  *  *  *  * * *  *  *  *  *  * * 2 | 0 0 0 1 0 0 0 0 1
----------------------+----------------+------------------------------------+-------------------------------------------+------------------
x.... x....5o....     ♦ 10  0  0  0  0 | 5 10  0 0  0  0  0  0  0 0  0 0  0 | 5 2  0  0  0  0  0 0 0  0  0  0  0  0 0 0 | 1 * * * * * * * *
xx... xo... .....&#x  ♦  4  2  0  0  0 | 2  2  4 1  0  0  0  0  0 0  0 0  0 | 1 0  2  2  0  0  0 0 0  0  0  0  0  0 0 0 | * 5 * * * * * * *
xxx.. ..... ofx..&#xt ♦  2  4  4  0  0 | 1  0  4 2  4  2  0  2  0 0  0 0  0 | 0 0  2  0  2  2  0 0 1  0  0  0  0  0 0 0 | * * 5 * * * * * *
..... xoxfo5ofxox&#xt ♦  5  5 10  5  5 | 0  5 10 0 10  0  5  5 10 0 10 0  5 | 0 1  0  5  5  0  5 0 0  0  5  5  0  5 0 1 | * * * 2 * * * * *
.xx.. .ox.. .....&#x  ♦  0  2  4  0  0 | 0  0  0 1  4  2  2  0  0 0  0 0  0 | 0 0  0  0  0  2  2 1 0  0  0  0  0  0 0 0 | * * * * 5 * * * *
..xxx ..xfo .....&#xt ♦  0  0  4  4  2 | 0  0  0 0  0  2  2  0  4 2  4 1  0 | 0 0  0  0  0  0  0 1 0  2  2  0  2  0 0 0 | * * * * * 5 * * *
..xx. ..... ..xo.&#x  ♦  0  0  4  2  0 | 0  0  0 0  0  2  0  2  4 1  0 0  0 | 0 0  0  0  0  0  0 0 1  2  0  2  0  0 0 0 | * * * * * * 5 * *
...xx ..... ...ox&#x  ♦  0  0  0  2  4 | 0  0  0 0  0  0  0  0  0 1  4 2  2 | 0 0  0  0  0  0  0 0 0  0  0  0  2  2 1 0 | * * * * * * * 5 *
....x ....o5....x     ♦  0  0  0  0 10 | 0  0  0 0  0  0  0  0  0 0  0 5 10 | 0 0  0  0  0  0  0 0 0  0  0  0  0  0 5 2 | * * * * * * * * 1
```