

genus ^{c}  3, orientable 
Schläfli formula ^{c}  {3,7} 
V / F / E ^{c}  24 / 56 / 84 
notes  
vertex, face multiplicity ^{c}  1, 1 
21, each with 8 edges 24, each with 7 edges 28, each with 6 edges 42, each with 4 edges 21, each with 8 edges  
antipodal sets  8 of ( 3v ), 28 of ( 2f ), 21 of ( 4e ) 
rotational symmetry group  PSL(2,7), with 168 elements 
full symmetry group  PSL(2,7)×C2, with 336 elements 
its presentation ^{c}  < r, s, t  t^{2}, r^{‑3}, (rs)^{2}, (rt)^{2}, (st)^{2}, s^{‑7}, (rs^{‑2})^{4} > 
C&D number ^{c}  R3.1 
The statistics marked ^{c} are from the published work of Professor Marston Conder. 
Its dual is
Its Petrie dual is
It can be 2split to give
It can be rectified to give
Its 2hole derivative is
Its 3hole derivative is
It can be stellated (with path <>/2) to give
It can be stellated (with path <1,1>) to give
It can be stellated (with path <2,2>) to give
It can be stellated (with path <>/3) to give
List of regular maps in orientable genus 3.
Its skeleton is 7valent Klein graph.
This regular map is related to the small cubicuboctahedron and the group M24.
For a version of the diagram with the vertices labelled as in the "roadmap", click here.
Orientable  
Nonorientable 
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