Acronym tikit
Name triakis tetrahedron,
apiculated tetrahedron
 
 ©
Inradius 5/sqrt(88) = 0.533002
Vertex figure [t6], [T3]
Dihedral angles
  • at long edge:   arccos(-7/11) = 129.521196°
  • at short edge:   arccos(-7/11) = 129.521196°
Dual tut
External
links
wikipedia   polytopewiki   mathworld  

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  [t6]
.o3.o3.o    | * 4 | 0  3 |  3  [T3]
------------+-----+------+---
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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