What is the name of this hexagon/pentagon polyhedron?
What is the name of this convex polyhedron?
$(V,E,F)=(14,36,24)$.
The top and bottom vertices are degree-$6$, spanning hexagons, which are zigzag connected in the band between the two hexagons. The faces are approximate isosceles triangles in this physical model.
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