VTRMC 2015 Problem 2

The planar diagram below, with equilateral triangles and regular hexagons, sides length $2$ cm, is folded along the dashed edges of the polygons, to create a closed surface in three-dimensional Euclidean spaces. Edges on the periphery of the planar diagram are identified (or glued) with precisely one other edge on the periphery in a natural way. Thus, for example, $BA$ will be joined to $QP$ and $AC$ will be joined to $DC$ . Find the volume of the three-dimensional region enclosed by the resulting surface.