Starting from the generic second level tetraflexagon map, which consists of a node linked to four surrounding nodes, any of the linked nodes can be dropped for a total of sixteen possibilities, not all of which are symmetrically independent. Thus one cound drop one node, an opposite or an adjacent pait, or three of the four. That makes six combinations, plus the full second order flexagon or just the full first order flexagon.

Amongst all of these, various possibilities for tubulations exist.