Acronym saddid
TOCID symbol dID
Name small dodekicosidodecahedron
 
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Circumradius sqrt[sqrt(5)+11/4] = 2.232951
Vertex figure [3/2,10,5,10]
Snub derivation
General of army srid
Colonel of regiment srid
Dihedral angles
  • between {5} and {10}:   arccos(-1/sqrt(5)) = 116.565051°
  • between {3} and {10}:   arccos(sqrt[(5+2 sqrt(5))/15]) = 37.377368°
External
links
hedrondude   wikipedia   WikiChoron   mathworld

As abstract polytope saddid is isomorphic to gaddid, sidditdid, and gidditdid, thereby replacing retrograde pentagons and decagons respectively by pentagrams and decagrams, by retrograde pentagrams and decagons, by pentagons and decagrams. – As such saddid is a lieutenant.

The small dodekicosidodecahedron is an edge-faceting of the small rhombicosidodecahedron (srid).


Incidence matrix according to Dynkin symbol

x3/2o5x5*a

.   . .    | 60 |  2  2 |  1  2  1
-----------+----+-------+---------
x   . .    |  2 | 60  * |  1  1  0
.   . x    |  2 |  * 60 |  0  1  1
-----------+----+-------+---------
x3/2o .    |  3 |  3  0 | 20  *  *
x   . x5*a | 10 |  5  5 |  * 12  *
.   o5x    |  5 |  0  5 |  *  * 12

x5/4o3x5*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*a | 10 |  5  5 |  * 12  *
.   o3x    |  3 |  0  3 |  *  * 20

β3o5x

both( . . . ) | 60 |  2  2 |  1  1  2
--------------+----+-------+---------
both( . . x ) |  2 | 60  * |  0  1  1
sefa( β3o . ) |  2 |  * 60 |  1  0  1
--------------+----+-------+---------
      β3o .     3 |  0  3 | 20  *  *
both( . o5x ) |  5 |  5  0 |  * 12  *
sefa( β3o5x ) | 10 |  5  5 |  *  * 12

starting figure: x3o5x

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