Meaning of vertex figure | Babel Free

Definitions

The figure exposed when a corner of a polyhedron or polytope is sliced off.

Examples

“1970, Harold Scott Macdonald Coxeter, Twisted Honeycombs, Conference Board⟳ of the Mathematical Sciences, Regional Conference Series in Mathematics: Number⟳ 4, American Mathematical Society, page 14, Thus the vertex figure⟳ of a polygon is the line-segment whose end-points are the vertex figures of the two edges at one vertex, the vertex figure⟳ of a polyhedron or tessellation {p, q} is the polygon {q} whose edges are the vertex figures of the q faces at one vertex, and the analogous "vertex figure⟳" of the honeycomb of cubes (§1) is the polyhedron whose faces are the vertex figures of the eight cubic cells that come⟳ together at one vertex.”

“Now try⟳ to see⟳ which of these vertex figures cannot be continued to give⟳ a semiregular tiling of the whole plane.”

“At each vertex of a tessellation, the vertex figure⟳ is the polygon formed by joining in order⟳ the mid-points of all edges incident with the vertex. A tessellation of a surface for which all the participating polygons and vertex figures are regular and equal is termed a regular tessellation.”

CEFR level