There is a public pool at Rinconada Park. You can learn more about the pool at :http://www.cityofpaloalto.org/gov/depts/csd/recreation/aquatics/default.asp
It is in Rinconada Park at the Community Center. You can also find the Junior Museum, Palo Alto Children's Library, Palo Alto Children's Theatre, and the Lucy Stern Theatre at the Community Center.
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