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)
External links

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