Tangential 1-blocks over GF(3)

In a fundamental paper on the algebraic theory of graph colouring Tutte [2] proves that the only tangential 1-block over GF(2) is the geometry corresponding to the polygon matroid of the graph K"3. For a good discussion of the problem and a direct proof of Tutte's theorem see Aigner [1, p. 373]. The purpose of this note is to prove the following result.