## Prisms

If you stack equal figures, you get a prisms, which are symmetric with respect to the center plane. I used figures with rotational symmetry or symmetry with respect to one or two lines. This way I got constructions with up to three planes of symmetry and rotational symmetry.

Unfortunately it's impossible to construct a prism using all pieces, because the number of layers is even or the area of the cross-section is even, contrary to the conditions for constructions..

For some cross-sections I tested, whether a prism of given height is possible to construct with the stacked tetrahexes. If a solution was found, it's indicated by a +. If a solution is impossible, the prism got a -. The prisms with a ? seem to be impossible, too, but I haven't got a proof.

## Triangular Cross-section

Shape of Cross-section Area of Cross-section Hight / Number of Hexagons / Solvable
T2 3 4/12/+, 8/24/+ , 12/36/-
T3 6 2/12/+, 4/24/+, 6/36/+, 8/48/+, 10/60/+, 12/72/+ , 14/84/-
T4 10 2/20/+, 4/40+, 6/60+, 8/80/+
T5 15 4/60/+
T6 21 4/84/+
T7 28 1/28/-, 2/54/+, 3/72/+
T8 36 1/36/-, 2/72/+

## Hexagonal Cross-section

Shape of Cross-section Area of Cross-section Hight / Number of Hexagons / Solvable
H2 7 4/28+, 8/56/+ , 12/84/-
H3 19 4/76/+

## Rhombic Cross-section

Shape of Cross-section Area of Cross-section Hight / Number of Hexagons / Solvable
RH2 4 1/4/+, 2/8/+, 3/12/+, 4/16/+, 5/20/+, 6/24/+, 7/28/+, 8/32/+, 9/36/+, 10/40/+ , 11/44/?, 15/60/-
RH3 9 4/36/+, 8/72/+
RH4 16 1/16/+, 2/32/+, 3/48/+, 4/80/+
RH6 36 1/36/-, 2/72/+

## Rectangular Cross-section

Shape of Cross-section Area of Cross-section Hight / Number of Hexagons / Solvable
R 3 4 3 10 2/20/+, 4/40/+, 6/60/+, 8/80/+
R 7 8 7 22 2/44/+, 4/88/+
R 9 10 9 28 1/28/+, 2/56/+, 3/84/+
Z 11 12 11 34 1/34/-, 2/68/+
R 3 2 3 8 1/8/-, 2/16/+, 3/24/+,...,10/80/+ , 11/88/-
R 4 3 4 11 4/44/+, 8/88+
R 11 10 11 32 1/32/-, 2/64/+
R 13 12 13 38 2/76/+
R 2 3 2 3 2 12 1/12/+, 2/24/+,...,7/84/+
R 3 4 3 4 3 17 4/68/+
R 4 5 4 5 4 22 2/44/+, 4/88/+
R 2 1 2 1 2 8 1/8/-, 2/16/+, 3/16/+,...8/64/+ , 9/72/?, 10/80/-
r 6 5 6 5 6 28 1/28/+, 2/56/+, 3/84/+
R 8 7 8 7 8 38 1/38/-, 2/76/+

The maximum height of the prisms in the table is 12. If you allow an asymmetric cross-section even a height of 14 can be achieved.

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