# Example of C-rigid polytopes which are not B-rigid

In: Mathematica Slovaca, vol. 69, no. 2
Suyoung Choi - Kyoungsuk Park

## Details:

Year, pages: 2019, 437 - 448
Keywords:
cohomologically rigid, B-rigid, quasitoric manifold, simple polytope, Peterson graph
A simple polytope $P$ is said to be \emph{B-rigid} if its combinatorial structure is characterized by its Tor-algebra, and is said to be \emph{C-rigid} if its combinatorial structure is characterized by the cohomology ring of a quasitoric manifold over $P$. It is known that a B-rigid simple polytope is C-rigid. In this paper, we show that the B-rigidity is not equivalent to the C-rigidity.