Acronym	gaddip
Name	great-dodecahedron prism
Cross sections	©
Circumradius	sqrt[(7+sqrt(5))/8] = 1.074481
General of army	ipe
Colonel of regiment	ipe
Dihedral angles	at {5} between gad and pip:   90° at {4} between pip and pip:   arccos(1/sqrt(5)) = 63.434949°
Face vector	24, 72, 54, 14
Confer	general polytopal classes: Wythoffian polychora
External links

As abstract polytope gaddip is isomorphic to sissiddip, thereby replacing pentagons by pentagrams resp. replacing gad by sissid and pip by stip. – As such gaddip is a lieutenant.

Incidence matrix according to Dynkin symbol

x x5o5/2o

. . .   . | 24 |  1  5 |  5  5 |  5 1
----------+----+-------+-------+-----
x . .   . |  2 | 12  * |  5  0 |  5 0
. x .   . |  2 |  * 60 |  1  2 |  2 1
----------+----+-------+-------+-----
x x .   . |  4 |  2  2 | 30  * |  2 0
. x5o   . |  5 |  0  5 |  * 24 |  1 1
----------+----+-------+-------+-----
x x5o   . ♦ 10 |  5 10 |  5  2 | 12 *
. x5o5/2o ♦ 12 |  0 30 |  0 12 |  * 2

snubbed forms: β2β5o5/2o

x x5o5/3o

. . .   . | 24 |  1  5 |  5  5 |  5 1
----------+----+-------+-------+-----
x . .   . |  2 | 12  * |  5  0 |  5 0
. x .   . |  2 |  * 60 |  1  2 |  2 1
----------+----+-------+-------+-----
x x .   . |  4 |  2  2 | 30  * |  2 0
. x5o   . |  5 |  0  5 |  * 24 |  1 1
----------+----+-------+-------+-----
x x5o   . ♦ 10 |  5 10 |  5  2 | 12 *
. x5o5/3o ♦ 12 |  0 30 |  0 12 |  * 2

x x5/4o5/2o

. .   .   . | 24 |  1  5 |  5  5 |  5 1
------------+----+-------+-------+-----
x .   .   . |  2 | 12  * |  5  0 |  5 0
. x   .   . |  2 |  * 60 |  1  2 |  2 1
------------+----+-------+-------+-----
x x   .   . |  4 |  2  2 | 30  * |  2 0
. x5/4o   . |  5 |  0  5 |  * 24 |  1 1
------------+----+-------+-------+-----
x x5/4o   . ♦ 10 |  5 10 |  5  2 | 12 *
. x5/4o5/2o ♦ 12 |  0 30 |  0 12 |  * 2

x x5/4o5/3o

. .   .   . | 24 |  1  5 |  5  5 |  5 1
------------+----+-------+-------+-----
x .   .   . |  2 | 12  * |  5  0 |  5 0
. x   .   . |  2 |  * 60 |  1  2 |  2 1
------------+----+-------+-------+-----
x x   .   . |  4 |  2  2 | 30  * |  2 0
. x5/4o   . |  5 |  0  5 |  * 24 |  1 1
------------+----+-------+-------+-----
x x5/4o   . ♦ 10 |  5 10 |  5  2 | 12 *
. x5/4o5/3o ♦ 12 |  0 30 |  0 12 |  * 2

xx5oo5/2oo&#x   → height = 1
(gad || gad)

o.5o.5/2o.    | 12  * |  5  1  0 |  5  5  0 | 1  5 0
.o5.o5/2.o    |  * 12 |  0  1  5 |  0  5  5 | 0  5 1
--------------+-------+----------+----------+-------
x. ..   ..    |  2  0 | 30  *  * |  2  1  0 | 1  2 0
oo5oo5/2oo&#x |  1  1 |  * 12  * |  0  5  0 | 0  5 0
.x ..   ..    |  0  2 |  *  * 30 |  0  1  2 | 0  2 1
--------------+-------+----------+----------+-------
x.5o.   ..    |  5  0 |  5  0  0 | 12  *  * | 1  1 0
xx ..   ..&#x |  2  2 |  1  2  1 |  * 30  * | 0  2 0
.x5.o   ..    |  0  5 |  0  0  5 |  *  * 12 | 0  1 1
--------------+-------+----------+----------+-------
x.5o.5/2o.    ♦ 12  0 | 30  0  0 | 12  0  0 | 1  * *
xx5oo   ..&#x ♦  5  5 |  5  5  5 |  1  5  1 | * 12 *
.x5.o5/2.o    ♦  0 12 |  0  0 30 |  0  0 12 | *  * 1