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It looks like the vertex arrangement is a pentagonal antiprism, except different diameter pentagons on top and bottom. Tom Ruen (talk) 06:57, 19 April 2014 (UTC)[reply]
Yes, it is. Bowers would probably call it a pentagonal antipodium, and it looks like the verf of padohi (the runcinated icosahedral 120-cell), but has different edge lengths. Double sharp (talk) 07:22, 19 April 2014 (UTC)[reply]