The smallest polyhex tetrads use tetrahexes. The first, by Scott Kim, is from Gardner's book.
The smallest tetrads for polyhexes with vertical mirror symmetry use 7-hexes:
The smallest tetrads for polyhexes with birotary symmetry around a cell use 9-hexes:
The smallest tetrad for polyhexes with ternary symmetry uses 9-hexes:
The smallest tetrad for polyhexes with ternary symmetry about a cell uses 13-hexes:
The smallest holeless tetrad for symmetric polyhexes uses 9-hexes:
Last revised 2018-11-14.