There are a few websites with lists and/or databases of graphs, maps and polytopes.

• House of graphs has a searchable database of interesting graphs and aims to serve as a repository for lists of graphs and graph generators,
• Encyclopedia of graphs is an online encyclopedia of graph collections with some data about different families of graphs,
• Database of graphs in combinatorica format,

There are several censuses of symmetric objects (for example Marston Conder, Dimitri Leemans, Primož Potočnik).

I would also like to know about other websites of similar nature out there, since I'm working on one myself. It's still an early stage project, but has some use already. It aims to one day be able to provide a platform for computational attempts for all sorts of discrete objects (you can see some features for the exploratory aspect on the website).

There are a few websites with lists and/or databases of graphs, maps and polytopes.

• House of graphs has a searchable database of interesting graphs and aims to serve as a repository for lists of graphs and graph generators,
• Encyclopedia of graphs is an online encyclopedia of graph collections with some data about different families of graphs,
• Database of graphs in combinatorica format,
• Encyclopedia of Finite Graphs is a "set of tools and data to compute all known invariants for simple connected graphs".

There are several censuses of symmetric objects (for example Marston Conder, Dimitri Leemans, Primož Potočnik).

I would also like to know about other websites of similar nature out there, since I'm working on one myself. It's still an early stage project, but has some use already. It aims to one day be able to provide a platform for computational attempts for all sorts of discrete objects (you can see some features for the exploratory aspect on the website).