Acronym dope, K-4.74 Name dodecahedron prism Segmentochoron display Cross sections ` ©` Circumradius sqrt[(11+3 sqrt(5))/8] = 1.487792 Coordinates (τ/2, τ/2, τ/2, 1/2)   & all permutations in all but last coord., all changes of sign (vertex inscribed f-cube) (τ2/2, 1/2, 0, 1/2)   & even permutations, all changes of sign where τ = (1+sqrt(5))/2 General of army (is itself convex) Colonel of regiment (is itself locally convex – no other uniform polychoral members) Externallinks

As abstract polytope dope is isomorphic to gissiddip, thereby replacing pentagons by pentagrams resp. replacing doe by gissid and pip by stip.

Incidence matrix according to Dynkin symbol

```x o3o5x

. . . . | 40 |  1  3 |  3  3 |  3 1
--------+----+-------+-------+-----
x . . . |  2 | 20  * |  3  0 |  3 0
. . . x |  2 |  * 60 |  1  2 |  2 1
--------+----+-------+-------+-----
x . . x |  4 |  2  2 | 30  * |  2 0
. . o5x |  5 |  0  5 |  * 24 |  1 1
--------+----+-------+-------+-----
x . o5x ♦ 10 |  5 10 |  5  2 | 12 *
. o3o5x ♦ 20 |  0 30 |  0 12 |  * 2
```

```x o3o5/4x

. . .   . | 40 |  1  3 |  3  3 |  3 1
----------+----+-------+-------+-----
x . .   . |  2 | 20  * |  3  0 |  3 0
. . .   x |  2 |  * 60 |  1  2 |  2 1
----------+----+-------+-------+-----
x . .   x |  4 |  2  2 | 30  * |  2 0
. . o5/4x |  5 |  0  5 |  * 24 |  1 1
----------+----+-------+-------+-----
x . o5/4x ♦ 10 |  5 10 |  5  2 | 12 *
. o3o5/4x ♦ 20 |  0 30 |  0 12 |  * 2
```

```x o3/2o5x

. .   . . | 40 |  1  3 |  3  3 |  3 1
----------+----+-------+-------+-----
x .   . . |  2 | 20  * |  3  0 |  3 0
. .   . x |  2 |  * 60 |  1  2 |  2 1
----------+----+-------+-------+-----
x .   . x |  4 |  2  2 | 30  * |  2 0
. .   o5x |  5 |  0  5 |  * 24 |  1 1
----------+----+-------+-------+-----
x .   o5x ♦ 10 |  5 10 |  5  2 | 12 *
. o3/2o5x ♦ 20 |  0 30 |  0 12 |  * 2
```

```x o3/2o5/4x

. .   .   . | 40 |  1  3 |  3  3 |  3 1
------------+----+-------+-------+-----
x .   .   . |  2 | 20  * |  3  0 |  3 0
. .   .   x |  2 |  * 60 |  1  2 |  2 1
------------+----+-------+-------+-----
x .   .   x |  4 |  2  2 | 30  * |  2 0
. .   o5/4x |  5 |  0  5 |  * 24 |  1 1
------------+----+-------+-------+-----
x .   o5/4x ♦ 10 |  5 10 |  5  2 | 12 *
. o3/2o5/4x ♦ 20 |  0 30 |  0 12 |  * 2
```

```oo3oo5xx&#x   → height = 1
(doe || doe)

o.3o.5o.    | 20  * |  3  1  0 |  3  3  0 | 1  3 0
.o3.o5.o    |  * 20 |  0  1  3 |  0  3  3 | 0  3 1
------------+-------+----------+----------+-------
.. .. x.    |  2  0 | 30  *  * |  2  1  0 | 1  2 0
oo3oo5oo&#x |  1  1 |  * 20  * |  0  3  0 | 0  3 0
.. .. .x    |  0  2 |  *  * 30 |  0  1  2 | 0  2 1
------------+-------+----------+----------+-------
.. o.5x.    |  5  0 |  5  0  0 | 12  *  * | 1  1 0
.. .. xx&#x |  2  2 |  1  2  1 |  * 30  * | 0  2 0
.. .o5.x    |  0  5 |  0  0  5 |  *  * 12 | 0  1 1
------------+-------+----------+----------+-------
o.3o.5x.    ♦ 20  0 | 30  0  0 | 12  0  0 | 1  * *
.. oo5xx&#x ♦  5  5 |  5  5  5 |  1  5  1 | * 12 *
.o3.o5.x    ♦  0 20 |  0  0 30 |  0  0 12 | *  * 1
```