The V-Flex, Triangle Orientation and Catalan Numbers in Hexaflexagons
College Mathematics Journal
Regular hexaflexagons mysteriously change faces as you pinch flex them. This paper describes a different flex, the V-flex, which allows the hexahexaflexagon (with only 9 faces under the pinch flex) to have 3420 faces. The article goes on to explain the classification of triangle orientations in a hexaflexagon and to give an example of flexagon combinatorics.
Iacob, Ionut E., T. Bruce McLean, Hua Wang.
"The V-Flex, Triangle Orientation and Catalan Numbers in Hexaflexagons."
College Mathematics Journal, 43 (1): 6-10.