Concept
Crystal system — where it appears
One of the seven groupings of crystal classes by which holohedry each is contained in, so the system says what the lattice must be able to do. There are seven rather than thirty-two because a class and its lattice's symmetry are different objects.
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Twenty-five cells, and fourteen lattices
The usual picture of the fourteen Bravais lattices is a plate of fourteen boxes, which is the answer with the argument removed. The argument is one question asked of twenty-five candidates, and the question has a computable answer.
Forty-eight becomes sixteen
Centre one face of a cube and the four threefold axes along its body diagonals are gone. That sentence is usually offered as a fact to accept; it is a computation whose answer is a number, and the number says which lattice you got instead.
Named alongside it
The objects these essays reach for when they reach for this one.
CentringHolohedryLattice automorphismMetric tensorBody diagonalBravais latticeCell transformationSubgroup