Snub (geometry)

In geometry, a snub is an operation applied to a polyhedron. The term originates from Kepler's names of two Archimedean solids, for the snub cube (cubus simus) and snub dodecahedron (dodecaedron simum). In general, snubs have chiral symmetry with two forms, with clockwise or counterclockwise orientations. By Kepler's names, a snub can be seen as an expansion of a regular polyhedron, with the faces moved apart, and twists on their centers, adding new polygons centered on the original vertices, and pairs of triangles fitting between the original edges.

The terminology was generalized by Coxeter, with a slightly different definition, for a wider set of uniform polytopes.

Conway snubs

John Conway explored generalized polyhedron operators, defining what is now called Conway polyhedron notation, which can be applied to polyhedra and tilings. Conway calls Coxeter's operation a semi-snub.

In this notation, snub is defined by the dual and gyro operators, as s = dg, and it is equivalent to an alternation of a truncation of an ambo operator. Conway's notation itself avoids Coxeter's alternation (half) operation since it only applies for polyhedra with only even-sided faces.

Geometry

Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of formal mathematical science emerging in the West as early as Thales (6th century BC). By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. In the classical world, both geometry and astronomy were considered to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.

Geometry (Ivo Perelman album)

Geometry is an album by Brazilian jazz saxophonist Ivo Perelman featuring American pianist Borah Bergman, which was recorded in 1996 and released on the English Leo label.

Reception

In his review for AllMusic, Alex Henderson says that "this CD doesn't quite fall into the 'essential' category... Nonetheless, Geometry is an enjoyable release that Perelman's more-devoted followers will want."

The Penguin Guide to Jazz notes that "Bergman is wily enough to find ways of both supporting and undercutting the mighty sound of the tenor."

Track listing

Personnel

References

Geometric group action

In mathematics, specifically geometric group theory, a geometric group action is a certain type of action of a discrete group on a metric space.

Definition

In geometric group theory, a geometry is any proper, geodesic metric space. An action of a finitely-generated group G on a geometry X is geometric if it satisfies the following conditions:

Uniqueness

If a group G acts geometrically upon two geometries X and Y, then X and Y are quasi-isometric. Since any group acts geometrically on its own Cayley graph, any space on which G acts geometrically is quasi-isometric to the Cayley graph of G.

Examples

Cannon's conjecture states that any hyperbolic group with a 2-sphere at infinity acts geometrically on hyperbolic 3-space.

References

Snub

A snub, cut or slight is a refusal to recognise an acquaintance by ignoring them, avoiding them or pretending not to know them. For example, a failure to greet someone may be considered a snub.

See also

References

Snub (disambiguation)

A snub is a refusal to recognise an acquaintance. It may also refer to:

SNUB

SNUB or Stop Norwich UrBanisation is a non-profit organisation based around Norwich, United Kingdom, whose aim is to stop the urbanisation of Norwich and its surrounding villages, such as Rackheath, Salhouse, Wroxham and Postwick.

The work of SNUB has received wide coverage, including national coverage on BBC Radio 4's Farming Today programme and in the UK newspaper, the Daily Telegraph. It has also received local coverage on television programmes such as BBC One's Politics Show,BBC One's Look East,ITV's Anglia Tonight and a BBC One Norwich North By-Election Special; and in local newspapers, such as the Eastern Daily Press and the Norwich Evening News.

In March 2012, after a successful legal challenge at the High Court, they announced that the actor Martin Shaw would become their official patron. In a press release, he announced that he was "simply furious and upset by your plight and that of all of us who wish to live in quiet and peace. I will be your Patron and keep fighting".

Rackheath Eco-town