Acronym dirid, J76
Name diminished rhombicosidodecahedron
 
 © ©    ©
Circumradius sqrt[sqrt(5)+11/4] = 2.232951
Vertex figures [4,5,10], [3,4,5,4]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
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°
  • between {4} and {10}:   arccos(-sqrt[(5-sqrt(5))/10]) = 121.717474°
  • between {5} and {10}:   arccos(-1/sqrt(5)) = 116.565051°
Confer
uniform relative:
srid  
related Johnson solids:
pecu   pabidrid   mabidrid   pagydrid   gyrid   tedrid  
general polytopal classes:
Johnson solids  
External
links
wikipedia   polytopewiki   mathworld   quickfur

This polyhedron is an edge-faceting of the small rhombicosidodecahedron (srid).


Incidence matrix according to Dynkin symbol

xxFofxx5xfoFxxo&#xt   → height(1,2) = height(5,6) = sqrt[(5+sqrt(5))/10] = 0.850651
                        height(2,3) = height(4,5) = height(6,7) = sqrt[(5-sqrt(5))/10] = 0.525731
                        height(3,4) = sqrt[(5-2 sqrt(5))/5] = 0.324920

o......5o......     | 10  * * *  *  * * | 1 1  1 0  0  0  0  0 0  0 0 0  0 0 | 1 1 1 0  0 0 0 0 0 0 0  at {10}
.o.....5.o.....     |  * 10 * *  *  * * | 0 0  1 1  1  1  0  0 0  0 0 0  0 0 | 0 1 1 1  1 0 0 0 0 0 0
..o....5..o....     |  *  * 5 *  *  * * | 0 0  0 0  2  0  2  0 0  0 0 0  0 0 | 0 0 1 0  2 1 0 0 0 0 0
...o...5...o...     |  *  * * 5  *  * * | 0 0  0 0  0  2  0  2 0  0 0 0  0 0 | 0 0 0 1  2 0 1 0 0 0 0
....o..5....o..     |  *  * * * 10  * * | 0 0  0 0  0  0  1  1 1  1 0 0  0 0 | 0 0 0 0  1 1 1 1 0 0 0
.....o.5.....o.     |  *  * * *  * 10 * | 0 0  0 0  0  0  0  0 0  1 1 1  1 0 | 0 0 0 0  0 0 1 1 1 1 0
......o5......o     |  *  * * *  *  * 5 | 0 0  0 0  0  0  0  0 0  0 0 0  2 2 | 0 0 0 0  0 0 0 0 2 1 1  at opposite {5}
--------------------+-------------------+------------------------------------+-----------------------
x...... .......     |  2  0 0 0  0  0 0 | 5 *  * *  *  *  *  * *  * * *  * * | 1 1 0 0  0 0 0 0 0 0 0
....... x......     |  2  0 0 0  0  0 0 | * 5  * *  *  *  *  * *  * * *  * * | 1 0 1 0  0 0 0 0 0 0 0
oo.....5oo.....&#x  |  1  1 0 0  0  0 0 | * * 10 *  *  *  *  * *  * * *  * * | 0 1 1 0  0 0 0 0 0 0 0
.x..... .......     |  0  2 0 0  0  0 0 | * *  * 5  *  *  *  * *  * * *  * * | 0 1 0 1  0 0 0 0 0 0 0
.oo....5.oo....&#x  |  0  1 1 0  0  0 0 | * *  * * 10  *  *  * *  * * *  * * | 0 0 1 0  1 0 0 0 0 0 0
.o.o...5.o.o...&#x  |  0  1 0 1  0  0 0 | * *  * *  * 10  *  * *  * * *  * * | 0 0 0 1  1 0 0 0 0 0 0
..o.o..5..o.o..&#x  |  0  0 1 0  1  0 0 | * *  * *  *  * 10  * *  * * *  * * | 0 0 0 0  1 1 0 0 0 0 0
...oo..5...oo..&#x  |  0  0 0 1  1  0 0 | * *  * *  *  *  * 10 *  * * *  * * | 0 0 0 0  1 0 1 0 0 0 0
....... ....x..     |  0  0 0 0  2  0 0 | * *  * *  *  *  *  * 5  * * *  * * | 0 0 0 0  0 1 0 1 0 0 0
....oo.5....oo.&#x  |  0  0 0 0  1  1 0 | * *  * *  *  *  *  * * 10 * *  * * | 0 0 0 0  0 0 1 1 0 0 0
.....x. .......     |  0  0 0 0  0  2 0 | * *  * *  *  *  *  * *  * 5 *  * * | 0 0 0 0  0 0 1 0 1 0 0
....... .....x.     |  0  0 0 0  0  2 0 | * *  * *  *  *  *  * *  * * 5  * * | 0 0 0 0  0 0 0 1 0 1 0
.....oo5.....oo&#x  |  0  0 0 0  0  1 1 | * *  * *  *  *  *  * *  * * * 10 * | 0 0 0 0  0 0 0 0 1 1 0
......x .......     |  0  0 0 0  0  0 2 | * *  * *  *  *  *  * *  * * *  * 5 | 0 0 0 0  0 0 0 0 1 0 1
--------------------+-------------------+------------------------------------+-----------------------
x......5x......     | 10  0 0 0  0  0 0 | 5 5  0 0  0  0  0  0 0  0 0 0  0 0 | 1 * * *  * * * * * * *
xx..... .......&#x  |  2  2 0 0  0  0 0 | 1 0  2 1  0  0  0  0 0  0 0 0  0 0 | * 5 * *  * * * * * * *
....... xfo....&#xt |  2  2 1 0  0  0 0 | 0 1  2 0  2  0  0  0 0  0 0 0  0 0 | * * 5 *  * * * * * * *
.x.o... .......&#x  |  0  2 0 1  0  0 0 | 0 0  0 1  0  2  0  0 0  0 0 0  0 0 | * * * 5  * * * * * * *
.oooo..5.oooo..&#xr |  0  1 1 1  1  0 0 | 0 0  0 0  1  1  1  1 0  0 0 0  0 0 | * * * * 10 * * * * * *  cycle(BCED)
....... ..o.x..&#x  |  0  0 1 0  2  0 0 | 0 0  0 0  0  0  2  0 1  0 0 0  0 0 | * * * *  * 5 * * * * *
...ofx. .......&#xt |  0  0 0 1  2  2 0 | 0 0  0 0  0  0  0  2 0  2 1 0  0 0 | * * * *  * * 5 * * * *
....... ....xx.&#x  |  0  0 0 0  2  2 0 | 0 0  0 0  0  0  0  0 1  2 0 1  0 0 | * * * *  * * * 5 * * *
.....xx .......&#x  |  0  0 0 0  0  2 2 | 0 0  0 0  0  0  0  0 0  0 1 0  2 1 | * * * *  * * * * 5 * *
....... .....xo&#x  |  0  0 0 0  0  2 1 | 0 0  0 0  0  0  0  0 0  0 0 1  2 0 | * * * *  * * * * * 5 *
......x5......o     |  0  0 0 0  0  0 5 | 0 0  0 0  0  0  0  0 0  0 0 0  0 5 | * * * *  * * * * * * 1

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