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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 is to be made. Cards have been designed; below are images of recent drafts. The 132 Steiner cards are divided into six suits of 22 cards (see StackExchange). It is anticipated that bridge-size cards, 2¼″×3½″ ≈ 57mm×89mm, will be printed by MakePlayingCards.com. The plan is that decks will be available for purchase by geeks.

Each deck is planned to comprise 144 cards:

132 Steiner cards, being 22 of each of six suits. Each card has two different presentations of the letters: a list of six characters; 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 must be removed.

One card giving credit and explanation, with “

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

Also, I have asked: on Math.StackExchange, how inform group theorists?.

Search for #SteinerKirkmanCards on Google.

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

There follow low-resolution images of drafts of some of the cards. Constructive comment welcomed.

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):

And also the current draft of the back of all the cards:

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