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A sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups. All the other finite simple groups form 18 infinite families numbered by q - power of prime number and n - natural number. Sporadic groups attach attention due to their sporadic/exceptional nature - similar to exceptional Lie groups. The first sporadic groups were found by Mathieu in 1860s. The last sporadic group J4 was discovered in 1975 by Janko.

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What is the geometric shape of the Monster sporadic group?

It is not too surprising that the Monster group $M$ is the symmetry group of something geometrical. E.g. every group is the group of symmetries of some convex polytope. You can even make it a vertex- …
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