
genus ^{c}  1, nonorientable 
Schläfli formula ^{c}  {4,3} 
V / F / E ^{c}  6 / 4+3 / 12 
notes  This is not a regular map, it has faces of two kinds (it is quasiregular). 
rotational symmetry group  S4, with 24 elements 
full symmetry group  S4, with 24 elements 
its presentation ^{c}  < r, s, t  r^{2}, s^{2}, t^{2}, (rs)^{4}, (st)^{3}, (rt)^{2}, (srst)^{2} > 
It is the result of rectifying
It is the result of rectifying
List of regular maps in nonorientable genus 1.
This can be immersed in 3space as the tetrahemihexahedron or regular heptahedron, used as an example in chapter 2 of Proofs and Refutations by Imre Lakatos.
Orientable  
Nonorientable 
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