xkcd 2125 titled "Luna 2" refers to the object shown below. All faces seem to be pentagons. (found in this question.)
Copy of the Soviet pennant sent on the Luna 2 probe to the moon, at the Kansas Cosmosphere, Source
Question: What is the name of the polyhedral shape of the Soviet pennant on the Luna 2 spacecraft?
note: This question is about the shape without the spherical caps, the way that the underlying shape of a football is a truncated icosahedron. In this case though I am not sure if this shape will be a polyhedron or not as the five vertices of the pentagonal faces may not lay in a plane.
"Comparison of a truncated icosahedron with the typical appearance of a football/soccer ball." Source




as a 72 faced object, it's a canonical pentagonal heptacontakaidihedron or dokaiheptacontaheron
In Conway terms, it's a spherical quinto dodecahedron 'C969qD'
play with it here
However, I've not seen much about quinto outside the wikidpedia page and that viewer, so I'm no longer so sure about it. Another Conway recipe, 't5oD' is very similar.