# semiregular

## English

### Etymology

semiregular (not comparable)

1. Somewhat regular; occasional.
• 2007 July 24, Bill Finley, “Victorious Night for Lester in His Return From Cancer”, in New York Times[1]:
Although Lester must still see doctors on a semiregular basis for checkups, his health has returned to normal.
2. (topology, of a topological space) Whose regular open sets form a base.
• 1970, Stephen Willard, General Topology, 2004, page 98,
A space is semiregular iff the regularly open sets (3D) form a base for the topology. [] Every space X can be embedded in a semiregular space.
3. (geometry, of a polyhedron or tessellation of the plane) Uniform (isogonal and isotoxal) with regular faces of two or more types, such that each vertex is surrounded by the same polygons in the same order.
• 1993, H. Terrones, A. L. MacKay, The Geometry of Hypothetical Curved Graphite Structures, H. W. Kroto, J.E. Fischer, Deann Cox (editors), The Fullerenes, page 115,
It will be seen below that this semiregular polyhedron is of importance in its relationship to periodic minimal surfaces serving as a conceptual reference.
• 1998, David A. Singer, Geometry: Plane and Fancy, page 35,
In a semiregular tessellation, there is an isometry of the plane carrying any vertex to any other vertex.
• 2003, Saul Stahl, Geometry from Euclid to Knots, 2010, page 272,
While one of the semiregular polyhedra was mentioned by Plato, their first serious study is attributed to Archimedes.
• 2011, Tom Bassarear, Mathematics for Elementary School Teachers, page 583,
One that we will consider here is the semiregular tessellation—a tessellation of two or more regular polygons that are arranged so that the same polygons appear in the same order around each vertex point. The tessellation at the left in Figure 9.38 is a semiregular tessellation because the two figures are a square and a regular octagon. The tessellation at the right in Figure 9.38 is not a semiregular tessellation because the two figures are a square and a nonregular octagon. [] There are only eight possible semiregular tessellations.

#### Usage notes

In geometry, usage is sometimes inconsistent. In regard to 3-dimensional polyhedra, convexity is often implicitly assumed, and the infinite classes of prisms and antiprisms may also be omitted, leaving just the Archimedean solids. Conversely, others choose the path of inclusion, admitting figures such as certain nonconvex (but still uniform) star polyhedra, as well as the duals of all included polyhedra. (See Semiregular polyhedron on Wikipedia.Wikipedia )