- Distinguished Professor of Mathematics (and former Co-Director of the
New Zealand Institute of Mathematics and its Applications (the
NZIMA))

- Email: m.conder@auckland.ac.nz

- Telephone: +64 9 9238879

- Fax: +64 9 3737457

- Office: Rm 417 SMIS/Physics building

- all orientable regular maps on surfaces of genus 2 to 101, up to isomorphism and duality, with defining relations for their automorphism groups
- all non-orientable regular 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 [WARNING: this is a 4.34MB file!]
- 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 reflexible orientable regular 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 non-orientable regular 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 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) [WARNING: this is a 4.0MB file!]
- all
large groups of automorphisms
of compact Riemann surfaces of genus 2 to 101, up to equivalence of the group action,
listed by the
**type**of Fuchsian group (with triangular or quadrangular signature), along with defining relators (normal generators for the kernel) [WARNING: this is a 22.8MB file!] - all
large groups of automorphisms
of compact Riemann surfaces of genus 2 to 101, up to equivalence of the group action,
listed by
**genus**, along with the type of Fuchsian group (with triangular or quadrangular signature), and group defining relators (normal generators for the kernel) [WARNING: this is a 25.6MB file!] - a summary of the maximum orders of group actions on compact Riemann surfaces of genus 2 to 301, with signature types for the actions that have the maximum order
- a summary of the maximum orders of group actions on compact non-orientable Klein surfaces of genus 3 to 302, with signature types for the actions that have the maximum order
- a summary of the strong symmetric genus of all groups of order 2 to 127, including the signature types for the actions of the group on (orientable) surfaces of the corresponding genus
- a list of all the finite groups with strong symmetric genus 2 to 32, including the signature types for the actions of the group on (orientable) surfaces of the corresponding genus
- a summary of the symmetric genus of all groups of order 2 to 127, including the signature types for the actions of the group on (orientable) surfaces of the corresponding genus
- a list of all the finite groups with symmetric genus 2 to 32, including the signature types for the actions of the group on (orientable) surfaces of the corresponding genus
- a summary of the symmetric cross-cap number of all groups of order 2 to 127, including the signature types for the actions of the group on (non-orientable) surfaces of the corresponding genus
- a list of all the finite groups with symmetric cross-cap number 3 to 65, including the signature types for the actions of the group on (non-orientable) surfaces of the corresponding genus

- all trivalent (cubic) symmetric graphs on up to 2048 vertices, up to isomorphism, categorised by their type, and with a link to a 6.1Mb gzipped directory containing all the graphs themselves
- all trivalent (cubic) symmetric graphs on up to 10000 vertices, up to isomorphism, categorised by their type, etc.
- all symmetric graphs of order 2 to 30, up to isomorphism, with some information about their automorphism groups.
- all symmetric graphs of order 2 to 47, up to isomorphism, and given by their edge-sets, with some information about their automorphism groups.
- all symmetric graphs of order 2 to 47, up to isomorphism, and given by the neighbours of each vertex, with some information about their automorphism groups.

- summary of all trivalent (cubic) semi-symmetric graphs on up to 10000 vertices, up to isomorphism, listed by order, and then by Goldschmidt type.

- all regular polytopes with up to 2000 flags, up to isomorphism and duality, ordered by the number of flags under each rank, excluding those of rank 2 (regular polygons) and the degenerate examples that have a '2' in their Schlaefli symbol
- all regular polytopes with up to 2000 flags, up to isomorphism and duality, ordered by their type under each rank, excluding those of rank 2 (regular polygons) and the degenerate examples that have a '2' in their Schlaefli symbol
- all chiral polytopes with up to 2000 flags, up to isomorphism, reflection and duality, ordered by the number of flags under each rank
- all chiral polytopes with up to 2000 flags, up to isomorphism, reflection and duality, ordered by their type under each rank

- The New Zealand Mathematical Society
- The New Zealand Journal of Mathematics
- The Group Pub Forum
- The World Combinatorics Exchange
- The Graph Theory White Pages
- Gordon Royle's Combinatorial catalogues
- The Mathematics Genealogy Project website.

Prof. M.D.E. Conder

Department of Mathematics

University of Auckland

Private Bag 92019, Auckland

NEW ZEALAND