TITLE: Name of this polyhedron with 17 faces
QUESTION [10 upvotes]: I recently saw a jungle gym in a playground constructed with ropes and small vertices. It formed a really strange polyhedron that I had never seen before. I've searched all over for it, but cannot find it.

It:

Is convex
Consists of 2 pentagons, 10 hexagons, 5 squares, 17 faces total
Appears that each polygon is regular (or approximately so)

The polyhedron is constructed as follows:

Start with a regular pentagon.
Attach a regular hexagon to each edge of the pentagon.
Fold each hexagon so that it meets with its neighboring hexagon.
Mark the free edge of each hexagon that is parallel to the pentagon.
Construct a copy of the above.
Connect the two halves together where the hexagons are marked.
The space between the connected hexagons should form squares

REPLY [6 votes]: Topologically the polyhedron is a truncated pentagonal bipyramid: the pentagons are the truncated degree-$5$ vertices and the "squares" are the truncated degree-$4$ ones. But the photo shows two irregularities: the top-left and bottom-right hexagons appear slightly puckered and the lengths of edges adjacent to a pentagon vertex (which I will call type A edges) are slightly longer than the other edges (type B). There is no requirement for the faces to be flat or edge lengths to be equal because you want to grip the edges, not the faces, of this physical construct. As such, the polyhedron's "regularity" is but a trick of the eye.
It is possible to achieve regular squares, regular pentagons, just-regular-enough hexagons and a round shape simply by making type A edges $10\%$ longer: