Rotary and regular maps and hypermaps of small genus

• all regular orientable maps on surfaces of genus 2 to 101, up to isomorphism and duality, with defining relations for their automorphism groups
• all regular non-orientable maps on surfaces of genus 2 to 202, up to isomorphism and duality, with defining relations for their automorphism groups
• all chiral (irreflexible) orientably-regular maps on surfaces of genus 2 to 101, up to isomorphism, duality and reflection, with defining relations for their automorphism groups
• all proper orientable regular hypermaps on surfaces of genus 2 to 101, up to isomorphism and triality, with defining relations for their automorphism groups
• all proper non-orientable regular hypermaps on surfaces of genus 2 to 202, up to isomorphism and triality, with defining relations for their automorphism groups
• all proper chiral orientably-regular hypermaps on surfaces of genus 2 to 101, up to isomorphism, triality and reflection, with defining relations for their automorphism groups
• all quotients of triangle groups that act on compact Riemann surfaces of genus 2 to 101, up to isomorphism, duality/triality and reflection, with defining relators (normal generators for the kernel)
• all regular orientable maps on surfaces of genus 2 to 301, up to isomorphism and duality, with defining relations for their automorphism groups
• all chiral (irreflexible) orientably-regular maps on surfaces of genus 2 to 301, up to isomorphism, duality and reflection, with defining relations for their automorphism groups
• all regular non-orientable maps of genus 2 to 602, up to isomorphism, duality and reflection, with defining relations for their automorphism groups
• all rotary maps on closed surfaces with up to 1000 edges, up to isomorphism and duality and other transformations (including Petrie duality and opposite, when the map is fully regular, and missor image when the map is chiral)
• all fully regular maps on closed surfaces with up to 1000 edges, up to isomorphism and transformation under the six "Wilson" operators (duality, Petrie duality, opposite, etc.)
• all chiral rotary maps on orientable surfaces with up to 1000 edges, up to isomorphism, mirror image and duality
• all orientably-regular maps with rotation group of order at most 400
• all orientably-regular maps with rotation group a non-dihedral group of order at most 400
• regular and orientably-regular maps on closed surfaces having small Euler characteristic, listed by their type, up to duality
• regular and orientably-regular maps on closed surfaces having small non-positive Euler characteristic, listed by their type, up to duality
• regular and orientably-regular maps on closed surfaces having small negative Euler characteristic, listed by their type, up to duality.

Author

Marston Conder
Department of Mathematics
University of Auckland
Private Bag 92019, Auckland
NEW ZEALAND