Fundamentals
Derivation of Lattice Systems in 2D
Lattice systems in 2D are identified based on their rotational symmetry elements. Watch the lattice naturally emerge through rotation and translation.
The 2D Lattices
Select a lattice type to animate its geometric derivation.
Step 1 of 4
Start with a single lattice point O.
Space Groups in 2D
The 17 Plane Groups Builder
Plane groups are formed by adding symmetry-compatible motifs to the lattice arrays. Watch the point group symmetry methodically build the fundamental basis step-by-step around the origin before replicating across space.
Sequential Basis Construction
Methodically construct the basis and map all structural symmetry.
Step 1 of X
Construct the lattice array.
Motif (Solid Comma)
Mirror (m)
Glide (g)