A connection game played on the curved surface of a cone. The goal is to create a closed loop from the player's edge to the centre, or to connect a path to the centre. The game can be played on a projection, which is isomorphic to the usual Hex rhombus with some cells overlapping or removed.
Conect is an exotic, two-player connection game played on the curved surface of a cone (not including the base). The edge is divided into two parts, colored red and blue. Conect has a well balanced geometry. Absent is the central region of concentrated influence common to most connection games. An ordinary hexagonal board will be used to explain the rules.
The two players, Red and Blue, take turns placing their own stones onto unoccupied cells of an initially empty board, one stone per turn, starting with Red. There are three ways to win:
To form a cone, take a hexagonally tessellated rhombus, and roll it up so that two adjacent edges coincide. If the two adjacent edges meet at an obtuse angle, a wide cone is formed. If the two adjacent edges meet at an acute angle, a narrow cone is formed. The corner between the joined edges (in both rhombuses) becomes the apex of the cone.
A board can be formed by projecting a cone onto a plane. Dale Walton drew a set of curved lines as a guide for drawing the cells of the projection. I found a polar equation to precisely represent said lines [r = sec (theta / 3)]. Noé Falzon (Castux) independently wrote his own equation and went on to complete illustrations of the projections of both the wide and narrow cones.
20240614 (2024-06-14). On Abstract Play since 2024-06-17.