What is the name of this hexagon/pentagon polyhedron?

I believe it is a gyroelongated hexagonal bipyramid.

https://en.wikipedia.org/wiki/Gyroelongated_bipyramid

The example shown in the Wikipedia article uses equilateral triangles, which results in coplanar faces around the degree-6 vertices, but as you mention, the model uses isosceles triangles.

From http://rcsr.anu.edu.au/polyhedra

I entered $14$ vertices and $24$ faces, and it seems to be a C14 Frank Kasper polyhedron (seems to be named from chemist researcher...)

The degrees of vertices $5$ and $6$ correspond.

http://rcsr.anu.edu.au/polyhedra/fkf

If I am right, the four extra faces make it a tetraicosahedron. But this is a generic term.