Acronym ...
Name sishi+idhi (?)
Circumradius 1
General of army ex
Colonel of regiment sishi
Confer idhi   gaghi+idhi   sishi   sishi+gaghi+120did   sishi+gaghi+idhi   sishi+paphicki+gridaphi   2sishi   2sishi+2paphicki  

Looks like a compound of a sishi with idhi. Its vertex figure is a variation of 2ike+gad, in fact f3/2v5o, which in turn looks to the exterior like a doe. Edges coincide by 3 and pentagrams come in coincident pairs.

As abstract polytope sishi+idhi is isomorphic to gaghi+idhi, thereby interchanging pentagrams and pentagons resp. replacing sissid by gad.


Incidence matrix according to Dynkin symbol

o5o3o5x5/3*b

. . . .      | 120 |   60 |   60  30 |  12  20
-------------+-----+------+----------+--------
. . . x      |   2 | 3600 |    2   1 |   1   2
-------------+-----+------+----------+--------
. o . x5/3*b |   5 |    5 | 1440   * |   1   1
. . o5x      |   5 |    5 |    * 720 |   0   2
-------------+-----+------+----------+--------
o5o . x5/3*b   12 |   30 |   12   0 | 120   *
. o3o5x5/3*b   20 |   60 |   12  12 |   * 120

o5o3o5/4x5/2*b

. . .   .      | 120 |   60 |   60  30 |  12  20
---------------+-----+------+----------+--------
. . .   x      |   2 | 3600 |    2   1 |   1   2
---------------+-----+------+----------+--------
. o .   x5/2*b |   5 |    5 | 1440   * |   1   1
. . o5/4x      |   5 |    5 |    * 720 |   0   2
---------------+-----+------+----------+--------
o5o .   x5/2*b   12 |   30 |   12   0 | 120   *
. o3o5/4x5/2*b   20 |   60 |   12  12 |   * 120

o5o3/2o5x5/2*b

. .   . .      | 120 |   60 |   60  30 |  12  20
---------------+-----+------+----------+--------
. .   . x      |   2 | 3600 |    2   1 |   1   2
---------------+-----+------+----------+--------
. o   . x5/2*b |   5 |    5 | 1440   * |   1   1
. .   o5x      |   5 |    5 |    * 720 |   0   2
---------------+-----+------+----------+--------
o5o   . x5/2*b   12 |   30 |   12   0 | 120   *
. o3/2o5x5/2*b   20 |   60 |   12  12 |   * 120

o5o3/2o5/4x5/3*b

. .   .   .      | 120 |   60 |   60  30 |  12  20
-----------------+-----+------+----------+--------
. .   .   x      |   2 | 3600 |    2   1 |   1   2
-----------------+-----+------+----------+--------
. o   .   x5/3*b |   5 |    5 | 1440   * |   1   1
. .   o5/4x      |   5 |    5 |    * 720 |   0   2
-----------------+-----+------+----------+--------
o5o   .   x5/3*b   12 |   30 |   12   0 | 120   *
. o3/2o5/4x5/3*b   20 |   60 |   12  12 |   * 120

o5/4o3o5x5/3*b

.   . . .      | 120 |   60 |   60  30 |  12  20
---------------+-----+------+----------+--------
.   . . x      |   2 | 3600 |    2   1 |   1   2
---------------+-----+------+----------+--------
.   o . x5/3*b |   5 |    5 | 1440   * |   1   1
.   . o5x      |   5 |    5 |    * 720 |   0   2
---------------+-----+------+----------+--------
o5/4o . x5/3*b   12 |   30 |   12   0 | 120   *
.   o3o5x5/3*b   20 |   60 |   12  12 |   * 120

o5/4o3o5/4x5/2*b

.   . .   .      | 120 |   60 |   60  30 |  12  20
-----------------+-----+------+----------+--------
.   . .   x      |   2 | 3600 |    2   1 |   1   2
-----------------+-----+------+----------+--------
.   o .   x5/2*b |   5 |    5 | 1440   * |   1   1
.   . o5/4x      |   5 |    5 |    * 720 |   0   2
-----------------+-----+------+----------+--------
o5/4o .   x5/2*b   12 |   30 |   12   0 | 120   *
.   o3o5/4x5/2*b   20 |   60 |   12  12 |   * 120

o5/4o3/2o5x5/2*b

.   .   . .      | 120 |   60 |   60  30 |  12  20
-----------------+-----+------+----------+--------
.   .   . x      |   2 | 3600 |    2   1 |   1   2
-----------------+-----+------+----------+--------
.   o   . x5/2*b |   5 |    5 | 1440   * |   1   1
.   .   o5x      |   5 |    5 |    * 720 |   0   2
-----------------+-----+------+----------+--------
o5/4o   . x5/2*b   12 |   30 |   12   0 | 120   *
.   o3/2o5x5/2*b   20 |   60 |   12  12 |   * 120

o5/4o3/2o5/4x5/3*b

.   .   .   .      | 120 |   60 |   60  30 |  12  20
-------------------+-----+------+----------+--------
.   .   .   x      |   2 | 3600 |    2   1 |   1   2
-------------------+-----+------+----------+--------
.   o   .   x5/3*b |   5 |    5 | 1440   * |   1   1
.   .   o5/4x      |   5 |    5 |    * 720 |   0   2
-------------------+-----+------+----------+--------
o5/4o   .   x5/3*b   12 |   30 |   12   0 | 120   *
.   o3/2o5/4x5/3*b   20 |   60 |   12  12 |   * 120

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