In a recent article Minimal Cohen-Macaulay Simplicial Complexes by Dao, Doolittle, and Lyle many examples of CM complexes (which happen to be minimal by there definition) are listed in Section 5. For example, included in the list are triangulations of $\mathbb{RP}^{2n}$ or the dunce hat. Some other interesting examples are A non-partitionable Cohen-Macaulay simplicial complex and A balanced non-partitionable Cohen-Macaulay complex which are recent counterexamples to the "partionability conjecture."

Edit: Since the question asks about both shellablitly and CM-ness it is perhaps worth noting that shellablity depends of the complex and not just the space. So, all spheres and balls are CM, but there are non-shellable examples of each.

In a recent article Minimal Cohen-Macaulay Simplicial Complexes by Dao, Doolittle, and Lyle many examples of CM complexes (which happen to be minimal by their definition) are listed in Section 5. For example, included in the list are triangulations of $\mathbb{RP}^{2n}$ or the dunce hat. Some other interesting examples are A non-partitionable Cohen-Macaulay simplicial complex and A balanced non-partitionable Cohen-Macaulay complex which are recent counterexamples to the "partionability conjecture."

Edit: Since the question asks about both shellablitly and CM-ness it is perhaps worth noting that shellablity depends of the particular simplicial complex and not just the geometric realization. So, all spheres and balls are CM, but there are non-shellable examples of each.

In a recent article Minimal Cohen-Macaulay Simplicial Complexes by Dao, Doolittle, and Lyle many examples of CM complexes (which happen to be minimal by there definition) are listed in Section 5. For example, included in the list are triangulations of $\mathbb{RP}^{2n}$ or the dunce hat. Some interesting examples are A non-partitionable Cohen-Macaulay simplicial complex and A balanced non-partitionable Cohen-Macaulay complex which are recent counterexamples to the "partionability conjecture."

In a recent article Minimal Cohen-Macaulay Simplicial Complexes by Dao, Doolittle, and Lyle many examples of CM complexes (which happen to be minimal by there definition) are listed in Section 5. For example, included in the list are triangulations of $\mathbb{RP}^{2n}$ or the dunce hat. Some other interesting examples are A non-partitionable Cohen-Macaulay simplicial complex and A balanced non-partitionable Cohen-Macaulay complex which are recent counterexamples to the "partionability conjecture."

Edit: Since the question asks about both shellablitly and CM-ness it is perhaps worth noting that shellablity depends of the complex and not just the space. So, all spheres and balls are CM, but there are non-shellable examples of each.