Swish is a SET like card game.

The cards are transparent with a 4×3 grid of colored dots and targets:
	1) Corners (4) are blue
	2) Middles (2) are Purple
	3) Thick Edges (4) are Orange
	4) Thin Edge (2) are Green
As per discussion encoding a dot as a 1, a target as a -1, and nothing as a zero. We can think of each card as a 4×3 grid with one 1 and one -1 and all the rest are zeros.

Pics and Symmetry

Clear[SwishColor]
SwishColor[i_,j_]:=Switch[{i,j},
{1,1},Blue,
{4,1},Blue,
{4,3}, Blue,
{1,3},Blue,
{1,2},Green,
{4,2},Green,
{2,2},Purple,
{3,2},Purple,
_,          Orange]
SwishShape[k_]:= Switch[k,
   1,Disk[#,1/5]&,
-1, {Disk[#,1/3],{White,Disk[#,1/5]}}&,
_, {}]  
SwishCardPic[A_]:= Graphics[
Table[
{SwishColor[i,j],SwishShape[A[[i,j]]][{j,i}]},
{i,1,4},{j,1,3}],
Frame->True,
PlotRange->{{0.5,3.5},{0.5,4.5}},
FrameTicks->None
]
Flip[A_]:= Reverse[A];
Turn[A_]:= Transpose[Reverse[Transpose[A]]];
ExpandedSwishCardPic[A_]:= GraphicsGrid[
{{SwishCardPic[A],SwishCardPic[Turn[A]]},
{SwishCardPic[Flip[A]],SwishCardPic[Flip[Turn[A]]]}},
Frame->True,
PlotRange->{{0.5,3.5},{0.5,4.5}},
FrameTicks->None
]

A1={
{1,1,-1},
{1,1,1},
{-1,-1,1},
{1,1,1}
};
ExpandedSwishCardPic[A1]

4^11

After expanding the representation we can order the cards in a canonical order and go from there.

Why are there sixty cards.

Each card has two possible symbols at each of 12 slots.  There are a total of (Binomial[12, 2])  = 66  possible cards if you do this. This is not 60!    Which 6 possible cards are missing?

(Binomial[12, 2])