rotation group: 60 elements; elements by order: {1: 1, 2: 15, 3: 20, 5: 24}
involutions (half-turns): 15
each half-turn reverses exactly 2 edges and fixes no vertex: True ; every edge is reversed by exactly one half-turn: True
each involution is the geometric half-turn about the axis through the midpoint of the reversed edge: True
for every vertex v: histogram of d(v, h(v)) over the 15 half-turns: {((1, 3), (3, 6), (4, 3), (5, 3))}
numbers of vertices at distance 0..5 from a vertex: {0: 1, 1: 3, 2: 6, 3: 6, 4: 3, 5: 1}
v=0: vertices at distance 2: [1, 2, 4, 14, 15, 16] ; images h(v) over the 15 half-turns (vertex: distance): [(3, 3), (5, 3), (6, 3), (7, 5), (7, 5), (7, 5), (8, 1), (9, 1), (10, 1), (11, 3), (12, 3), (13, 3), (17, 4), (18, 4), (19, 4)]
