  We construct new symmetric Hadamard matrices of orders $92,116$, and $172$.
While the existence of those of order $92$ was known since 1978, the orders
$116$ and $172$ are new. Our construction is based on a recent new
combinatorial array discovered by N. A. Balonin and J. Seberry. For order $116$
we used an adaptation of an algorithm for parallel collision search. The
adaptation pertains to the modification of some aspects of the algorithm to
make it suitable to solve a 3-way matching problem. We also point out that a
new infinite series of symmetric Hadamard matrices arises by plugging into the
GP array the matrices constructed by Xia, Xia, Seberry, and Wu in 2005.
