Acronym gidditdid
TOCID symbol eJE
Name great ditrigonary dodekicosidodecahedron,
great dodekified icosidodecahedron
 
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Circumradius sqrt[(17-3 sqrt(5))/8] = 1.134229
Vertex figure [3,10/3,5,10/3]
General of army tid
Colonel of regiment (is itself locally convex – other uniform polyhedral members: giddy   giid – other edge facetings)
Dihedral angles
  • between {3} and {10/3}:   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632°
  • between {5} and {10/3}:   arccos(-1/sqrt(5)) = 116.565051°
External
links
hedrondude   wikipedia   polytopewiki   WikiChoron   mathworld   Polyedergarten

As abstract polytope gidditdid seems to be isomorphic to sidditdid, saddid, and gaddid, thereby replacing pentagons and decagrams respectively by retrograde pentagrams and decagons, by retrograde pentagons and decagons, by pentagrams and decagrams. But in fact it is only isomorphic to sidditdid. This is because one hasn't only to consider the actual faces, but also the pseudo faces (holes) as well. Saddid and gaddid have square pseudo faces, while sidditdid and gidditdid have hexagonal holes instead.


Incidence matrix according to Dynkin symbol

x5/3x3o5*a

.   . .    | 60 |  2  2 |  2  1  1
-----------+----+-------+---------
x   . .    |  2 | 60  * |  1  1  0
.   x .    |  2 |  * 60 |  1  0  1
-----------+----+-------+---------
x5/3x .    | 10 |  5  5 | 12  *  *
x   . o5*a |  5 |  5  0 |  * 12  *
.   x3o    |  3 |  0  3 |  *  * 20

x5/4o3/2x5/3*a

.   .   .      | 60 |  2  2 |  1  2  1
---------------+----+-------+---------
x   .   .      |  2 | 60  * |  1  1  0
.   .   x      |  2 |  * 60 |  0  1  1
---------------+----+-------+---------
x5/4o   .      |  5 |  5  0 | 12  *  *
x   .   x5/3*a | 10 |  5  5 |  * 12  *
.   o3/2x      |  3 |  0  3 |  *  * 20

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