Acronym  tikit 
Name 
triakis tetrahedron, apiculated tetrahedron 
©  
Inradius  5/sqrt(88) = 0.533002 
Vertex figure  [t^{6}], [T^{3}] 
Dihedral angles 

Dual  tut 
External links 
Note that this polyhedron also is the hull of a complex of 5 tets of the small edge size. The vertices of the central tet of that complex thus define the shallow tips. Its edges are of the same size as the shorter edges of the hull, but would be completely internal.
The triangles {(t,t,T)} have vertex angles t = arccos(5/6) = 33.557310° resp. T = arccos(7/18) = 112.885380°.
Edge sizes used here are tT = x = 1 (short) resp. tt = a = 5/3 = 1.666667 (long).
Incidence matrix according to Dynkin symbol
m3m3o = ao3oo3ox&#zx → height = 0 a = 5/3 = 1.666667 o.3o.3o.  4 *  3 3  6 [t^{6}] .o3.o3.o  * 4  0 3  3 [T^{3}] +++ a. .. ..  2 0  6 *  2 a oo3oo3oo&#x  1 1  * 12  2 x +++ ao .. ..&#x  2 1  1 2  12 {(t,t,T)}
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