Heronian friezes and Pl\"ucker relations

Abstract

In this article, we use Pl\"ucker relations in the Grassmannian $Gr(3,n)$ to give relations that hold amongst some of the entries of the Heronian frieze of order $n$. Furthermore, we make a connection between certain subfriezes of a Heronian frieze and Pl\"ucker friezes $P(3,n)$, and then show that some determinants of the matrices whose elements lie in those subfriezes are vanishing.