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| genus c | 1, non-orientable |
| Schläfli formula c | {2,12} |
| V / F / E c | 1 / 6 / 6 |
| notes | 
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| vertex, face multiplicity c | 12, 1 |
| 1, with 12 edges 6, each with 2 edges 4, each with 3 edges 6, each with 2 edges 2, each with 6 edges 6, each with 2 edges 3, each with 4 edges 6, each with 2 edges 1, with 12 edges 6, each with 2 edges | |
| antipodal sets | 6 of ( 2f, 2h3, 2h5; 2p3 ), 6 of ( 2e, 2h2, 2h4, 2h6; 2p4 ), 4 of ( 2p2, 2p2 ) |
| rotational symmetry group | D24, with 24 elements |
| full symmetry group | D24, with 24 elements |
| its presentation c | < r, s, t | r2, s2, t2, (rs)6, (st)2, (rt)2 > |
| C&D number c | N1.n6 |
| The statistics marked c are from the published work of Professor Marston Conder. | |
Its dual is
Its Petrie dual is
It can be 2-fold covered to give
It can be rectified to give
It is its own 5-hole derivative.
It is the half shuriken of
List of regular maps in non-orientable genus 1.
Its skeleton is 6 . 1-cycle.
| Orientable | |
| Non-orientable |
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