The Mermin pentagram is a configuration of ten three-qubit observables arranged on the five lines of a pentagram.
Each line contains four mutually commuting observables, and each observable lies
on two lines. The product of the observables on four lines is the identity
matrix 
,
while the product on the fifth line is 
. It gives a state-independent parity proof of the Kochen-Specker
theorem (Mermin 1990, 1993).
For an explicit realization, let 
and 
denote the Pauli matrices 
and 
acting on qubit 
and the identity matrix
acting on the other two qubits. The five commuting contexts
can be taken as follows.
| context | observables | product |
| 1 |  ,  ,  ,  |  |
| 2 |  ,  ,  ,  |  |
| 3 |  ,  ,  ,  |  |
| 4 |  ,  ,  ,  |  |
| 5 |  ,  ,  ,  |  |
Suppose that a noncontextual assignment associates a value 
with every observable 
and reproduces the five context products. Multiplying its
five equations makes every value 
occur twice, so the left side is
 |
The product of the required signs on the right side is instead 
, a contradiction.
The anticommutation graph of the configuration is the Petersen graph. Its hypergram has ten vertices, five contexts,
contextuality degree 1, and tolerated error per context 
(Muller and Giorgetti 2025, Muller and Saniga 2026).
