The family was named by their Coxeter symbol k21 by its bifurcating Coxeter–Dynkin diagram, with a single ring on the end of the k-node sequence.
The sequence as identified by Gosset ends as an infinite tessellation (space-filling honeycomb) in 8-space, called the E8 lattice.
It is a tessellation of hyperbolic 9-space constructed of ∞ 9-simplex and ∞ 9-orthoplex facets with all vertices at infinity.)
The triangular prism and rectified 5-cell are included at the beginning for completeness.
The orthoplex faces are constructed from the Coxeter group Dn−1 and have a Schläfli symbol of {31,n−1,1} rather than the regular {3n−2,4}.