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Main link to MakePlayingCards.com at which sets of Steiner cards are for sale.

The author used to own a set of Steiner cards, made mid-1997. They had been laser printed onto white paper; laminated; and guillotined. That set, and many odd socks, have disappeared into the ether.

What is such a thing? Each card from such a Steiner(5, 6, 12) system has six letters from the first twelve of the alphabet, A … L, such that for any choice of five letters one card and only one card contains all five. Self-evidently, this is a thing of some mathematical elegance and symmetry. This mathematical toy is closely related to M₁₂, another beautifully symmetric abstract mathematical object.

The old deck was lost, so a new deck has been made. The 132 Steiner cards are divided into six suits of 22 cards (see StackExchange). MakePlayingCards.com has printed bridge-size cards = 2¼″×3½″ ≈ 57mm×89mm, and are available for purchase.

Each deck comprises 144 cards:

132 Steiner cards, being 22 of each of six suits. Each card has two different presentations of the letters: a 2×3 list of six characters; and a 4×3 box of twelve Booleans. For some games one presentation might be superior—player’s choice.

Eleven jokers: one of each suit; one of each colour; and two generic (one ‘light’ and one ‘dark’). Of course, it might be that for some games all or some jokers are removed or deemed equivalent—game designer’s choice.

One card giving credit and explanation, with “

*Please publish any interesting games devised for these cards, tagged ‘#SteinerKirkmanCards’.*”

Help wanted: by what non-intrusive non-spam means can group theorists be informed of this?

Search for #SteinerKirkmanCards on Google.

*— Julian D. A. WisemanLondon, September–December 2020*

There follow low-resolution images of some of the cards.

Example Steiner cards, one rotated 180°. Suits are arranged in chains of complementary pairs (StackExchange); the rulers show the card’s position within its chain.

And as if in a hand, to emphasise the 180° non-symmetry:

Also jokers, one for each suit (shown is the cross), one for each colour (blue), and two generic (dark). Jokers have a line on the top. Players may well hold their Steiner cards with matching orientations: corners showing either six letters or twelve Booleans. Hence jokers held in a random orientation might reveal their presence to other players, as a hand with non-consistent rotations of the card backs would be a hand containing joker(s). So that jokers can be held with orientation matching the non-jokers, they have a line at the top, of the same thicknes and length as that of the centre-placed twelve Booleans.

The back of all the cards:

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