> Quick browsing through tutorials led me to believe that only quads and hexes
> are supported. Are any other reference element shapes supported (triangles,
> prisms, tetrahedrons)?

No, only quads and hexes as you said. Also see the FAQ here:
http://dealii.sourceforge.net/index.php/Deal.II_Questions_and_Answers#Can_I_use.2Fimplement_triangles.2Ftetrahedra_in_deal.II.3F

-- 
Timo Heister
http://www.math.tamu.edu/~heister/
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