Acronym tedrid, J83
Name tridiminished rhombicosidodecahedron,
magnaursahedron
  
 © ©
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°
Face vector 45, 75, 32
Confer
uniform relative:
srid  
related Johnson solids:
pecu   dirid  
general polytopal classes:
Johnson solids  
External
links 		wikipedia   polytopewiki   mathworld   quickfur  

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


Incidence matrix

xxFVF(Vx)fo-3-ofxxf(oF)xx-&#xt   → height(1,2) = height(8,9) = sqrt[(3-sqrt(5))/6] = 0.356822
                                   height(2,3) = height(5,67) = height(67,8) = 1/sqrt(3) = 0.577350
                                   height(3,4) = height(4,5) = sqrt[(3+sqrt(5))/6] = 0.934172
                                   where F=ff=f+x, V=2f

o....(..)..-3-o....(..)..      | 3 * * * * * * * * | 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 0 0 0  upper {5} top vertex
.o...(..)..-3-.o...(..)..      | * 6 * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0 0 0 0  upper {5} lateral vertices
..o..(..)..-3-..o..(..)..      | * * 6 * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 0 0 1 1 1 0 0 0 0 0 0  upper {5} bottom vertices
...o.(..)..-3-...o.(..)..      | * * * 6 * * * * * | 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 | 0 0 0 1 1 1 0 0 0 0 0  medial {5} top vertices
....o(..)..-3-....o(..)..      | * * * * 6 * * * * | 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 | 0 0 0 1 0 1 1 0 0 0 0  medial {5} lateral vertices
.....(o.)..-3-.....(o.)..      | * * * * * 3 * * * | 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 | 0 0 0 0 0 1 2 1 0 0 0  medial {5} bottom vertex
.....(.o)..-3-.....(.o)..      | * * * * * * 6 * * | 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 | 0 0 0 1 0 0 1 0 1 0 0  lower {5} top vertices
.....(..)o.-3-.....(..)o.      | * * * * * * * 6 * | 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 | 0 0 0 0 0 0 1 1 1 1 0  lower {5} lateral vertices
.....(..).o-3-.....(..).o      | * * * * * * * * 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 1 2 1  lower {5} bottom vertex
-------------------------------+-------------------+---------------------------------+----------------------
x....(..)..   .....(..)..      | 2 0 0 0 0 0 0 0 0 | 3 * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0 0
oo...(..)..-3-oo...(..)..-&#x  | 1 1 0 0 0 0 0 0 0 | * 6 * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 0 0
.x...(..)..   .....(..)..      | 0 2 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * * | 0 1 0 1 0 0 0 0 0 0 0
.oo..(..)..-3-.oo..(..)..-&#x  | 0 1 1 0 0 0 0 0 0 | * * * 6 * * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0 0
.....(..)..   ..x..(..)..      | 0 0 2 0 0 0 0 0 0 | * * * * 3 * * * * * * * * * * * | 0 0 1 0 1 0 0 0 0 0 0
..oo.(..)..-3-..oo.(..)..-&#x  | 0 0 1 1 0 0 0 0 0 | * * * * * 6 * * * * * * * * * * | 0 0 1 0 1 0 0 0 0 0 0
.....(..)..   ...x.(..)..      | 0 0 0 2 0 0 0 0 0 | * * * * * * 3 * * * * * * * * * | 0 0 0 0 1 1 0 0 0 0 0
...oo(..)..-3-...oo(..)..-&#x  | 0 0 0 1 1 0 0 0 0 | * * * * * * * 6 * * * * * * * * | 0 0 0 1 0 1 0 0 0 0 0
....o(o.)..-3-....o(o.)..-&#x  | 0 0 0 0 1 1 0 0 0 | * * * * * * * * 6 * * * * * * * | 0 0 0 0 0 1 1 0 0 0 0
....o(.o)..-3-....o(.o)..-&#x  | 0 0 0 0 1 0 1 0 0 | * * * * * * * * * 6 * * * * * * | 0 0 0 1 0 0 1 0 0 0 0
.....(o.)o.-3-.....(o.)o.-&#x  | 0 0 0 0 0 1 0 1 0 | * * * * * * * * * * 6 * * * * * | 0 0 0 0 0 0 0 1 1 0 0
.....(.x)..   .....(..)..      | 0 0 0 0 0 0 2 0 0 | * * * * * * * * * * * 3 * * * * | 0 0 0 1 0 0 0 0 1 0 0
.....(.o)o.-3-.....(.o)o.-&#x  | 0 0 0 0 0 0 1 1 0 | * * * * * * * * * * * * 6 * * * | 0 0 0 0 0 0 1 0 1 0 0
.....(..)..   .....(..)x.      | 0 0 0 0 0 0 0 2 0 | * * * * * * * * * * * * * 3 * * | 0 0 0 0 0 0 0 1 0 1 0
.....(..)oo-3-.....(..)oo-&#x  | 0 0 0 0 0 0 0 1 1 | * * * * * * * * * * * * * * 6 * | 0 0 0 0 0 0 0 0 1 1 0
.....(..)..   .....(..).x      | 0 0 0 0 0 0 0 0 2 | * * * * * * * * * * * * * * * 3 | 0 0 0 0 0 0 0 0 0 1 1
-------------------------------+-------------------+---------------------------------+----------------------
x....(..)..-3-o....(..)..      | 3 0 0 0 0 0 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * *  top polar {3}
xx...(..)..   .....(..)..-&#x  | 2 2 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * *  {4}
.....(..)..   ofx..(..)..-&#xt | 1 2 2 0 0 0 0 0 0 | 0 2 0 2 1 0 0 0 0 0 0 0 0 0 0 0 | * * 3 * * * * * * * *  upper {5}
.xFVF(.x)..   .....(..)..-&#xt | 0 2 2 2 2 0 2 0 0 | 0 0 1 2 0 2 0 2 0 2 0 1 0 0 0 0 | * * * 3 * * * * * * *  {10}
.....(..)..   ..xx.(..)..-&#x  | 0 0 2 2 0 0 0 0 0 | 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 | * * * * 3 * * * * * *  {4}
.....(..)..   ...xf(o.)..-&#xt | 0 0 0 2 2 1 0 0 0 | 0 0 0 0 0 0 1 2 2 0 0 0 0 0 0 0 | * * * * * 3 * * * * *  medial {5}
....o(oo)o.-3-....o(oo)o.-&#xr | 0 0 0 0 1 1 1 1 0 | 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 | * * * * * * 6 * * * *  {4}
.....(..)..   .....(o.)x.-&#x  | 0 0 0 0 0 1 0 2 0 | 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 | * * * * * * * 3 * * *  {3}
.....(.x)fo   .....(..)..-&#xt | 0 0 0 0 0 0 2 2 1 | 0 0 0 0 0 0 0 0 0 0 0 1 2 0 2 0 | * * * * * * * * 3 * *  lower{5}
.....(..)..   .....(..)xx-&#x  | 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 | * * * * * * * * * 3 *  {4}
.....(..).o-3-.....(..).x      | 0 0 0 0 0 0 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * 1  bottom polar {3}

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