Stacked Squares and Rectangles

(by Peter F.Esser)

Name Parts per Piece Number of Pieces Constructions
Stacked Squares or Stacked Polyominoes
Stacked Tetrominoes
4 18 boxes, prisms,rings and frames, replicas of hexacubes
Stacked Pentominoes
5 78 are included in the pentomino section of my site
Stacked Hexominoes
6 477 no boxes! Under checkerboard coloring we have an even number of balanced pieces and an odd number of 2-4 pieces. Therefore we can't get a balanced box with all pieces.
Stacked Rectangles or Polyboxes
4 32 boxes, prisms with height 4 and 8, replicas of flat octarectangles
5 147 a cube, 3 congruent boxes, 3 congrunet stairs, 7 congruent prisms
6 934 no boxes! If we factorise the whole number of boxes we get 6*934 = 2*2*3*467. Each edge of a box containing all pieces must not be smaller than 6. Therefore a solution is impossible.