Catalyzes the conversion of 3-deoxy-D-arabino-heptulosonate 7-phosphate (DAHP) to dehydroquinate (DHQ). 7-phospho-2-dehydro-3-deoxy-D-arabino-heptonate = 3-dehydroquinate + phosphate Binds 1 divalent metal cation per subunit. Can use either Co(2+) or Zn(2+). Metabolic intermediate biosynthesis; chorismate biosynthesis; chorismate from D-erythrose 4-phosphate and phosphoenolpyruvate: step 2/7. Belongs to the sugar phosphate cyclases superfamily. Dehydroquinate synthase family.