p6 and p6m Snowflakes

thingiverse

This text demonstrates three snowflakes created using p6 and p6m, two-dimensional space groups characterized by six-fold rotation axes. The openSCAD code utilizes equivalent positions in these groups to place hexagons within a unit cell, with p6 offering six positions and p6m providing twelve. By generating adjacent unit cells, sets of seven or forty-nine can be formed. Hexagons can be replaced by any shape, while objects may be placed anywhere within the cell, adhering to space group symmetry rules. Examples include snowflake_p6m_c1.stl with six hexagons and one unit cell, snowflake_p6m_c7.stl consisting of four hexagons and seven unit cells, and snowflake_p6_c49.stl comprising three hexagons and forty-nine unit cells. Dxf and openSCAD files are provided for use. Snowflakes can be printed directly or with a raft on the build platform; the Replicator was used to print the examples at 1 shell and 50% infill, while snowflake_p6m_c7.stl required two shells and 50% infill. Instructions for generating snowflakes are included in the openSCAD code's beginning.