Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p.296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n≥5)
In Coxeter's "Regular Polytopes," the third edition published by Dover in New York in 1973 on page 296, Table I (iii), there are three regular polytopes in n-dimensional space where n is greater than or equal to five.