Acronym	gidtidap
Name	great-ditrigonary-icosidodecahedron antiprism
Cross sections	©
Circumradius	sqrt[(5+sqrt(5))/8] = 0.951057
Colonel of regiment	sidtidap
Face vector	40, 180, 184, 54
Confer	general polytopal classes: segmentochora
External links

As abstract polytope gidtidap is isomorphic to sidtidap, thereby replacing pentagons by pentagrams, resp. pap by stap and gidtid by sidtid.

In fact, this polychoron generalizes the idea of a 3D antiprism by way of being a snub (here: holosnub). But this figure is not what now became the accepted sense of a 4D antiprism, where its bases have to be duals of each other. It rather looks more like what was coined as cupola (in its narrower sense), i.e. the xoPoxQoo&#x segmentochora, as it uses pyramids and antiprisms for lacing facets. (But pyramids do point here in both directions, so.)

Incidence matrix according to Dynkin symbol

β2β5/2o3o

both( . .   . . ) | 40 |  3   6 |  3   9  3 |  3 1  4
------------------+----+--------+-----------+--------
both( s2s   . . ) |  2 | 60   * |  0   4  0 |  2 0  2
sefa( . β5/2o . ) |  2 |  * 120 |  1   1  1 |  1 1  1
------------------+----+--------+-----------+--------
      . β5/2o .   ♦  5 |  0   5 | 24   *  * |  1 1  0 
sefa( β2β5/2o . ) |  3 |  2   1 |  * 120  * |  1 0  1
sefa( . β5/2o3o ) |  3 |  0   3 |  *   * 40 |  0 1  1
------------------+----+--------+-----------+--------
      β2β5/2o .   ♦ 10 | 10  10 |  2  10  0 | 12 *  *
      . β5/2o3o   ♦ 20 |  0  60 | 12   0 20 |  * 2  *
sefa( β2β5/2o3o ) ♦  4 |  3   3 |  0   3  1 |  * * 40

starting figure: x x5/2o3o

xo5ox3/2oo3*a&#x   → height = sqrt[(sqrt(5)-1)/2] = 0.786151
(gidtid || gyro gidtid)

o. o.   o.       | 20  * |  6  3  0 |  3  3  6  3  0  0 | 1  3  3  1 0
.o .o   .o       |  * 20 |  0  3  6 |  0  0  3  6  3  3 | 0  3  1  3 1
-----------------+-------+----------+-------------------+-------------
x. ..   ..       |  2  0 | 60  *  * |  1  1  1  0  0  0 | 1  1  1  0 0
oo5oo3/2oo3*a&#x |  1  1 |  * 60  * |  0  0  2  2  0  0 | 0  2  1  1 0
.. .x   ..       |  0  2 |  *  * 60 |  0  0  0  1  1  1 | 0  1  0  1 1
-----------------+-------+----------+-------------------+-------------
x.5o.   ..       |  5  0 |  5  0  0 | 12  *  *  *  *  * | 1  1  0  0 0
x. ..   o.3*a    |  3  0 |  3  0  0 |  * 20  *  *  *  * | 1  0  1  0 0
xo ..   ..   &#x |  2  1 |  1  2  0 |  *  * 60  *  *  * | 0  1  1  0 0
.. ox   ..   &#x |  1  2 |  0  2  1 |  *  *  * 60  *  * | 0  1  0  1 0
.o5.x   ..       |  0  5 |  0  0  5 |  *  *  *  * 12  * | 0  1  0  0 1
.. .x3/2.o       |  0  3 |  0  0  3 |  *  *  *  *  * 20 | 0  0  0  1 1
-----------------+-------+----------+-------------------+-------------
x.5o.3/2o.3*a    ♦ 20  0 | 60  0  0 | 12 20  0  0  0  0 | 1  *  *  * *
xo5ox   ..   &#x ♦  5  5 |  5 10  5 |  1  0  5  5  1  0 | * 12  *  * *
xo ..   oo3*a&#x ♦  3  1 |  3  3  0 |  0  1  3  0  0  0 | *  * 20  * *
.. ox3/2oo   &#x ♦  1  3 |  0  3  3 |  0  0  0  3  0  1 | *  *  * 20 *
.o5.x3/2.o3*a    ♦  0 20 |  0  0 60 |  0  0  0  0 12 20 | *  *  *  * 1