# S4:{3,12}

### Statistics

 genus c 4, orientable Schläfli formula c {3,12} V / F / E c 6 / 24 / 36 notes vertex, face multiplicity c 3, 1 Petrie polygonsholes2nd-order Petrie polygons3rd-order holes3rd-order Petrie polygons4th-order holes4th-order Petrie polygons5th-order holes5th-order Petrie polygons6th-order holes 12, each with 6 edges6, each with 12 edges18, each with 4 edges24, each with 3 edges12, each with 6 edges12, each with 6 edges36, each with 2 edges24, each with 3 edges12, each with 6 edges18, each with 4 edges rotational symmetry group 72 elements. full symmetry group 144 elements. its presentation c < r, s, t | t2, r‑3, (rs)2, (rt)2, (st)2, (sr‑1s)3, srs‑3rs4 > C&D number c R4.1 The statistics marked c are from the published work of Professor Marston Conder.

### Relations to other Regular Maps

Its dual is S4:{12,3}.

Its Petrie dual is N20.3.

It can be 2-split to give R19.18.
It can be 4-split to give R49.67.
It can be 5-split to give R64.27′.
It can be 7-split to give R94.10′.

It can be obtained by triambulating S4:{6,6}3,2.

It is its own 5-hole derivative.

It can be stellated (with path <1,-1>) to give S4:{6,12} . The density of the stellation is 3.

### Underlying Graph

Its skeleton is 3 . K2,2,2.