Acronym	titdi
Name	tri-trigonally diminished icosahedron, (subsymmetrically) tristellated-dodecahedron, tri-kis-dodecahedron, dual of teddi, vertex figure of tridex
	©
Vertex figures	[K3], [T,K2], [k,t4], [T3]
Dual	teddi
Dihedral angles	at small edges v:   arccos(-1/sqrt(5)) = 116.565051° at medium edges f:   arccos(-1/sqrt(5)) = 116.565051° at long edges F:   arccos(-1/sqrt(5)) = 116.565051°
Face vector	8, 15, 9
Confer	related Johnson solids: teddi   uniform relative: doe   ike   general polytopal classes: subsymmetrical diminishings
External links

There is a vertex 4-coloring 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 f-edges 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((3-sqrt(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  [K3]
.o..3.o..         | * 3 * * | 1 2 0 0 | 2 1 0  [T,K2]
..o.3..o.         | * * 3 * | 0 2 2 1 | 1 2 2  [k,t4]
...o3...o         | * * * 1 | 0 0 0 3 | 0 0 3  [T3]
------------------+---------+---------+------
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)}