A 
triangular honeycomb board is an arrangement of hexagons
packed closely as in a honeycomb into a triangular shape with 
hexagons along the bottom, 
hexagons along the left angled side, and 
hexagons along the right angled side.
The most interesting and symmetrical such boards have 
(Konhauser et al. 1996, DeMaio and Tran 2013, Wagon
2014), making them "triangular triangular honeycomb boards," and may simply
be termed 
-triangular
honeycomb boards for short. 
-triangular honeycomb boards are illustrated above for small
.
-triangular
honeycomb boards are the basis for various graphs constructed on the basis of moves
by variations of chess pieces moving between hexagons.
The simplest of these is the triangular
honeycomb king graph, were a triangular grid king is allowed to move from a hexagon
to any adjacent hexagons. Connecting adjacent hexagon by edges then gives a graph
isomorphic (modulo indexing convention) with the 
-triangular grid graph,
as illustrated above for 
and 
.
