ordinary lattice:
    dimension:         3
    size parameter:    31
    generating vector: [1, 12, 3]
    definition:        lattice(31, [1, 12, 3])
embedded lattice:
    dimension:         3
    size parameter:    2^5
    generating vector: [1, 7, 9]
    definition:        lattice(2^5, [1, 7, 9])
