Acronym srid
TOCID symbol rID
Name small rhombicosidodecahedron
 
 © ©
Circumradius sqrt[sqrt(5)+11/4] = 2.232951
Vertex figure [3,4,5,4] = xf&#q
Vertex layers
LayerSymmetrySubsymmetries
 o3o5oo3o .o . o. o5o
1x3o5x x3o .
{3} first
x . x
{4} first
. o5x
{5} first
2 x3f . o . F . x5x
3a o3U . F . f . x5f
3b F3x .
4a f3F . V . o . F5o
4b f . U
5 U3x . U . F . o5F
6a x3U . x . W . f5x
6b W . x
7 F3f . F . V . x5x
8a U3o . x . W . x5o
opposite {5}
8b x3F . W . x
9 f3x . U . F  
10a o3x .
opposite {3}
V . o
10b f . U
11   F . f
12 o . F
13 x . x
opposite {4}
(F=ff, U=fu, V=x+ff, W=x+fu)
Coordinates
  1. 3/2, 1/2, 1/2)         & all permutations, all changes of sign
  2. (τ, τ2/2, τ/2)             & even permutations, all changes of sign
  3. 2/2, 1+τ/2, 0)        & even permutations, all changes of sign
where τ = (1+sqrt(5))/2
General of army (is itself convex)
Colonel of regiment (is itself locally convex – other uniform polyhedral members: saddid   sird – other edge facetings)
Dihedral angles
  • between {3} and {4}:   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843°
  • between {4} and {5}:   arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526°
Dual sladit
Confer
Grünbaumian relatives:
2srid  
related Johnson solids:
pecu   dirid   gyrid   pabidrid   mabidrid   pagydrid   magydrid   gybadrid   bagydrid   tagygrid   tedrid  
variations:
a3b5c   q3o5x   f3o5x   v3o5f  
External
links
hedrondude   wikipedia   WikiChoron   mathworld   Polyedergarten   quickfur

As abstract polytope srid is isomorphic to qrid, thereby replacing prograde pentagons by retrograde pentagrams.

Note that srid can be thought of as the external blend of 1 cube + 8 peppies + 12 bilbiros + 6 G3s, cf. the Steward toroid E5 \ 6J91(P4).


Incidence matrix according to Dynkin symbol

x3o5x

. . . | 60 |  2  2 |  1  2  1
------+----+-------+---------
x . . |  2 | 60  * |  1  1  0
. . x |  2 |  * 60 |  0  1  1
------+----+-------+---------
x3o . |  3 |  3  0 | 20  *  *
x . x |  4 |  2  2 |  * 30  *
. o5x |  5 |  0  5 |  *  * 12

snubbed forms: β3o5x, x3o5β, β3o5β

x5/4o3/2x 

.   .   . | 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   .   x |  4 |  2  2 |  * 30  *
.   o3/2x |  3 |  0  3 |  *  * 20

© 2004-2018
top of page