hemi-icosahedron: 10 blocks, every pair in exactly 2 blocks: True
edges: 25
min codegree: 3 | codegree values: [3, 5] | required floor((n-k+3)/2) = 3
tight Hamiltonian cycles (orders with the apex first, both directions): 0
adding one of the 10 missing triples creates a tight Hamiltonian cycle in 10 cases
