Acronym mabautid, J70
Name metabiaugmented truncated dodecahedron
 
 © ©
Vertex figure [3,4,5,4], [3,4,3,10], [3,102]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {4} (at join):   arccos(-sqrt[(5+2 sqrt(5))/15]) + arccos(sqrt[(5+sqrt(5))/10]) = 174.340106°
  • between {3} and {4} (pecu lacings):   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843°
  • between {4} and {10}:   arccos(-sqrt[(65-2 sqrt(5))/75]) = 153.942419°
  • between {4} and {5}:   arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526°
  • between {3} and {10}:   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632°
  • between {10} and {10}:   arccos(-1/sqrt(5)) = 116.565051°
Confer
uniform relative:
tid  
related Johnson solids:
pecu   autid   tautid  
general polytopal classes:
Johnson solids  
External
links
wikipedia   mathworld

Incidence matrix

2 * * * * * * * * * * * * * * * * * * * | 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  [3,102] top
* 4 * * * * * * * * * * * * * * * * * * | 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0  [3,4,3,10] topmost
* * 4 * * * * * * * * * * * * * * * * * | 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0  [3,4,5,4] upper
* * * 4 * * * * * * * * * * * * * * * * | 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0  [3,4,3,10]
* * * * 4 * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0  [3,102]
* * * * * 4 * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0  [3,4,5,4] medial
* * * * * * 4 * * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0  [3,4,3,10]
* * * * * * * 4 * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0  [3,102]
* * * * * * * * 2 * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 0 0 0 0 2 0 1 0 0 0 0 0 0  [3,4,5,4] lower
* * * * * * * * * 4 * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0  [3,4,3,10]
* * * * * * * * * * 2 * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0  [3,102]
* * * * * * * * * * * 4 * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0  [3,4,3,10] lowest
* * * * * * * * * * * * 4 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0  [3,102]
* * * * * * * * * * * * * 2 * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0  [3,102]
* * * * * * * * * * * * * * 4 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0  [3,102]
* * * * * * * * * * * * * * * 4 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0  [3,102]
* * * * * * * * * * * * * * * * 4 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0  [3,102]
* * * * * * * * * * * * * * * * * 4 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0  [3,102]
* * * * * * * * * * * * * * * * * * 4 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1  [3,102]
* * * * * * * * * * * * * * * * * * * 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1  [3,102] bottom
----------------------------------------+-----------------------------------------------------------------------+------------------------------------
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  {10}-{10}
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 4 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  {3}-{10}
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 2 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  {3}-{4} pecu,tid-join
0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 4 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0  {3}-{4}
0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 4 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0  {3}-{10} pecu,tid-join
0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * 2 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0  {4}-{5}
0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * 4 * * * * * * * * * * * * * * * * * * * * * * * * * * * * | 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0  {3}-{4}
0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * 4 * * * * * * * * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0  {4}-{5}
0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * 4 * * * * * * * * * * * * * * * * * * * * * * * * * * | 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0  {3}-{10}
0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * 4 * * * * * * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0  {3}-{4} pecu,tid-join
0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * 4 * * * * * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0  {3}-{10}
0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * 4 * * * * * * * * * * * * * * * * * * * * * * * | 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0  {10}-{10}
0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * 4 * * * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0  {3}-{4}
0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * 4 * * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0  {4}-{5}
0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * 4 * * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0  {3}-{4}
0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * 4 * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0  {3}-{10} pecu,tid-join
0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * 2 * * * * * * * * * * * * * * * * * * | 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0  {3}-{10}
0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * 4 * * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0  {3}-{10}
0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * 4 * * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0  {3}-{4}
0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * 4 * * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0  {3}-{4} pecu,tid-join
0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * 4 * * * * * * * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0  {3}-{10}
0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * * 2 * * * * * * * * * * * * * | 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0  {10}-{10}
0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * * * 2 * * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0  {3}-{10} pecu,tid-join
0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * * * * 4 * * * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0  {3}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * * * * * 4 * * * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0  {10}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * * * * * * 4 * * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0  {3}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 | * * * * * * * * * * * * * * * * * * * * * * * * * * 4 * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0  {3}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 | * * * * * * * * * * * * * * * * * * * * * * * * * * * 4 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0  {3}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 | * * * * * * * * * * * * * * * * * * * * * * * * * * * * 2 * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0  {3}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 | * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 4 * * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0  {3}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 | * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 4 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0  {3}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 | * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 4 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0  {10}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 | * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 2 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1  {3}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 | * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 4 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1  {3}-{10}
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 | * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0  {10}-{10}
----------------------------------------+-----------------------------------------------------------------------+------------------------------------
2 2 0 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 0 0 2 0 0 0 2 0 0 2 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * * * * * *  {10} upper
1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * * * * *  {3} tid
0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 2 * * * * * * * * * * * * * * *  {4}
0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 4 * * * * * * * * * * * * * *  {3} pecu
0 0 2 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 1 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 2 * * * * * * * * * * * * *  {5}
0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * 4 * * * * * * * * * * * *  {4}
0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * 4 * * * * * * * * * * *  {3} tid
0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 | 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 | * * * * * * * 4 * * * * * * * * * *  {10} equatorial
0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * 4 * * * * * * * * *  {3} pecu
0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * 4 * * * * * * * *  {4}
0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * 2 * * * * * * *  {3} tid
0 0 0 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * 2 * * * * * *  {3} pecu
0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * 4 * * * * *  {3} tid
0 0 0 0 0 0 0 0 0 0 0 2 2 0 2 0 0 2 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 0 0 2 0 0 0 2 1 0 0 | * * * * * * * * * * * * * 2 * * * *  {10} lower tropal
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 | * * * * * * * * * * * * * * 2 * * *  {3} tid
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 | * * * * * * * * * * * * * * * 4 * *  {3} tid
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 0 2 1 | * * * * * * * * * * * * * * * * 2 *  {10} lowest
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * * * * * * * 2  {3} tid

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