different between semiregular vs icosidodecahedron

English

Alternative forms

• semi-regular

Etymology

semi- +? regular

Adjective

semiregular (not comparable)

1. Somewhat regular; occasional.
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 )

Further reading

• List of convex uniform tilings on Wikipedia.Wikipedia
• Semiregular polyhedron on Wikipedia.Wikipedia
• Semiregular polytope on Wikipedia.Wikipedia
• Semiregular space on Wikipedia.Wikipedia
• Semiregular Polyhedron on Wolfram MathWorld
• Semiregular Tessellation on Wolfram MathWorld

English

Noun

icosidodecahedron (plural icosidodecahedra or icosidodecahedrons)

1. An Archimedean solid with thirty-two regular faces (twelve pentagons and twenty triangles).
   • 1961, The New Yorker, Volume 37, Part 4, page 172,

     […] together to form not only regular polyhedrons but rhombicosidodecahedrons, truncated icosidodecahedrons, and such.

   • 1992, Jean-Louis Verger-Gaugry, Quasicrystals and the Concept of Interpenetration in m35-approximant Crystals with Long-range Icosahedral Atomic Clustering, A. R. Yavari, Ordering and Disordering in Alloys, Elsevier Applied Science, page 498,

     A succession of 10 concentric icosidodecahedra centered at (0, 0, 0), forming a geometric sequence (the n^th one is ?ⁿ larger than the first one), is also put into evidence.

   • 2004, Marc-Alain Ouaknin, The Mystery of Numbers, unnumbered page,

     Thus, there is a star octahedron, three star dodecahedrons, and fifty-nine star icosidodecahedrons.

   • 2009, Walter Steurer, Sofia Deloudi, Crystallography of Quasicrystals: Concepts, Methods and Structures, page 306,

     The dark-gray (online: red) icosahedra are part of the B clusters, the light-gray dodecahedra of the B’ clusters, and the (online: blue) icosidodecahedra of the M clusters.

   • 2010, Debra Ann Ross, Master Math: Geometry, Cengage Learning, page 306,

     Polyhedrons include prisms; pyramids; the Platonic solids, including tetrahedrons, cubes, octahedrons, dodecahedrons, and icosahedrons; the Archimedean solids, such as cuboctahedrons and icosidodecahedrons; and the Johnson solids, such as square pyramids and triangular cupolas (dome-shape).

Derived terms

• rhombicosidodecahedron
• truncated icosidodecahedron

Translations