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 (GP 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.
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