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) Dual ite Dihedral angles at {4} between pip and pip:   arccos(-1/sqrt(5)) = 116.565051° at {5} between doe and pip:   90° Confer decompositions: ike || dope   general polytopal classes: segmentochora Externallinks

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

Note that dope can be thought of as the external blend of 20 pens + 30 squascs + 12 pippies + 2 ikadoes. This decomposition is described as the degenerate segmentoteron ox xo3oo5ox&#x.

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

snubbed forms: β2o3o5β
```

```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
```

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