tetragonal C is tetragonal P, and here is the cell change
The change of cell that carries the C-centred tetragonal description onto the P description of tetragonal: turn the axes through 45° and shrink by √2: the centred cell's own primitive cell is square. The new cell vectors, written in the old basis, are a′ = (1/2, 1/2, 0), b′ = (-1/2, 1/2, 0) and c′ = (0, 0, 1). All three conditions hold, which is what makes this a duplicate rather than a fifteenth lattice.
2 essays call
cell-change. The drawing above is what it returns with no arguments at all; every
call below passes it something, because a placement that passes nothing draws whichever member
of the family the generator happens to default to rather than the one its essay argues about.
Every one of this site's 393 essays names its parameters at the
call site, which the standard pass of 2026-08-09 established and param-floor
holds.
Where it is called
Changing this generator changes every one of these figures.
Lattices
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.
Lattices
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.