An incomplete Kal-toh.
A completed Kal-toh.
Kal-toh is a Vulcan game of intense strategy that can be played solitarily or by multiple individuals. The object of kal-toh, as stated by Tuvok, "Is not about striving for balance but about finding the seeds of order even in the midst of profound chaos." A kal-toh set consists of a number of playing rods called t'an.
When described by Harry Kim to an amnesic Tuvok, he said 'The object of the game was to turn this jumble of rods into a perfect sphere', and that each player takes turns to position pieces, the one managing to form the final intended shape winning. (VOY: "Riddles")
When Harry Kim referred to kal-toh as "Vulcan chess", Tuvok commented that, "Kal-toh is to chess as chess is to tic-tac-toe." (VOY: "Alter Ego")
- A different game referred to as Vulcan chess was shown in TAS: "The Magicks of Megas-Tu".
In a holodeck simulation created by the Doctor that included numerous historical figures, the holograms of Socrates and T'Pau played kal-toh together. (VOY: "Darkling")
During a game played by Tuvok and Harry Kim, Seven of Nine took a turn for Harry and beat Tuvok in one move, claiming she used elementary spatial harmonics to do so. (VOY: "The Omega Directive")
Tuvok, Icheb and Harry Kim often had a match of kal-toh together. Icheb was quite talented with the game. (VOY: "Endgame")
In an alternate timeline, Captain Harry Kim kept a kal-toh game in his ready room aboard the USS Rhode Island. (VOY: "Endgame")
Trivia
A completed game of kal-toh is in the shape of two nested icosidodecahedra connected by the centerpoints of their edges.