Acronym  titdi 
Name 
tritrigonally diminished icosahedron, (subsymmetrically) tristellateddodecahedron, trikisdodecahedron, dual of teddi, vertex figure of tridex 
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Vertex figures  [K^{3}], [T,K^{2}], [k,t^{4}], [T^{3}] 
Dual  teddi 
Dihedral angles 

Confer 

There is a vertex 4coloring of ike. Diminishing the vertices of a single color then derives teddi by chopping off 3 peppies. Diminishing the vertices of 2 such colors derives bitdi; peppies then already would intersect, this is where the fedges originate from. Diminishing 3 colors will result in the polyhedron, the dual of teddi, and at all 4 colors results in the dual of ike, i.e. in doe.
The faces are kites {(k,K,K,K)} with corner angle k = 36° and K = 108°, where side KK has size v = (sqrt(5)1)/2 = 0.618034, diagonal KK has size x = 1, side kK has size f = (1+sqrt(5))/2 = 1.618034, and diagonal kK has size sqrt[(5+sqrt(5))/2] = 1.902113, resp. golden triangles {(T,t,t)} with the same corner angles t = 36° and T = 108°, where side tT has the same size f, while side tt has size F = (3+sqrt(5))/2 = 2.618034.
Incidence matrix according to Dynkin symbol
oxoo3ooFo&#(v,f,f)t → height(1,2) = sqrt((3sqrt(5))/3) = 0.504623 height(2,3) = sqrt(sqrt(5)/3) = 0.863340 height(3,4) = 1/sqrt(3) = 0.577350 o...3o...  1 * * *  3 0 0 0  3 0 0 [K^{3}] .o..3.o..  * 3 * *  1 2 0 0  2 1 0 [T,K^{2}] ..o.3..o.  * * 3 *  0 2 2 1  1 2 2 [k,t^{4}] ...o3...o  * * * 1  0 0 0 3  0 0 3 [T^{3}] +++ oo..3oo..&#v  1 1 0 0  3 * * *  2 0 0 .oo.3.oo.&#f  0 1 1 0  * 6 * *  1 1 0 .... ..F.  0 0 2 0  * * 3 *  0 1 1 ..oo3..oo&#f  0 0 1 1  * * * 3  0 0 2 +++ oxo. ....&#(v,f)t  1 2 1 0  2 2 0 0  3 * * {(k,K,K,K)} .... .oF.&#f  0 1 2 0  0 2 1 0  * 3 * {(T,t,t)} .... ..Fo&#f  0 0 2 1  0 0 1 2  * * 3 {(T,t,t)}
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