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Steiner hexad cards: #SteinerKirkmanCards

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 The plan is that decks will be available for purchase by geeks.

Each deck is planned to comprise 144 cards:

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

Search for #SteinerKirkmanCards on Google.

— Julian D. A. Wiseman
London, 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:

Six characters Twelve Booleans

Also jokers, one for each suit (shown is the cross), one for each colour (blue), and two generic (dark):

Joker_Cross Joker_Blue Joker_Dark

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

Card back

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