Main index Other Papers index About author

Valid HTML 4.01 Transitional Valid CSS

Steiner hexad cards: #SteinerKirkmanCards

Main link to 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). has printed bridge-size cards = 2¼″×3½″ ≈ 57mm×89mm, and are available for purchase.

Each deck comprises 144 cards:

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

Search for #SteinerKirkmanCards on Google.

— Julian D. A. Wiseman
London, 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:

Six characters Twelve Booleans

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.

Joker_Cross Joker_Blue Joker_Dark

The back of all the cards:

Card back

Main index Top About author