# -: G :-

general*
n the Bower's army, the polytope that members of an army notionally shares vertices with. In practice, this is defined as the convex hull of the set of vertices.
genus*
A number designating how many equilivant holes a hedrix or 2-manifold has.
The theory of holes is much more complex in higher dimensions, and in practice, genus is used to fill in defects where Euler's surtope-polynomial fails for polyhedra.
geodesic *
A great circle (pro-flat) on the surface of the earth (pro-all-space) in space (real all-space).
This generalises to isocurves drawn with the same curvature as a larger isocurve in some larger space.
globlutope *
A name used for spheres of N dimensions, treating these as globular polytopes. So a globluchoron is a globular polychoron or 4-sphere.
The current style is glomofold.
glome *
A name used by George Olshevsky for a 4-sphere (glomochorix).
glomo *
The new style of name for spheres of n dimensions, is to treat the surface as being bent into the shape of a ball.
glomogon *
The result of inscribing consecutive edges as equal chords of a given circle. Polygons are quantum glomogons: that is, there are a finite number of edges so inscribed. In practice, such polygons are {oo/oo}, and might be written by a real number, eg {3.1415926535898}
When the number is rational, zB {2.5}, it may represent any polygon that reduces to this, zB, {10/4} or as well as .
glomohedrix *
A two-dimensional surface bent to positive curvature, such as the surface of a sphere. See hedrix.
A glomohedron is a figure bounded by a glomohedrix. Thus, we might refer to the surface of a sphere (as a space S2), as a glomohedrix, but the sphere with solid content is a glomohedron.
glomos *
An adjective implying the described polytope follows a finite closure sphere. For example, a dodecahedron {5,3} is a glomos polyhedron, regardless of the space it is embedded in.
The contrast here is that a hyperbolic dodecahedron is one that is in hyperbolic space, but the general shape of the dodecahedron follows a glomosphere, and is therefore glomos.
golden ratio φ *
A ratio of 1:φ.
While golden is established in this meaning, the use of distinct names for mathematical ratios is to be discouraged.
A golden rectangle is a rectangle x2f, of sides 1:φ.
A golden hexagon is a hexagon x3f, of alternating sides 1:φ.
The golden under- and over- truncates are fPxQo and xPfQo, zb the golden undertruncated icosahedron is f3x5o, consisting of golden hexagons and pentagons of unit edge.
goldfish revenge *
Lem Chastain's delightful geometric restriction that implies we ought use spherical constructions exclusively.
In a way, this helps to detangle the nature of parallelism into its constituant segments. When one adds the embedded inversive, one gets all of the elements elegantly.
-gon *
A corner, specifically formed by two arms. The word [gon] means knee. In practice, a polygon is reckoned by its vertices.
An alternate expression by polylatron is available.
Isogonal means a polytope with equal vertces, regardless of the dimensions: a polyhedron might be isogonal.
gonglotope*
A name proposed for a n-sphere with its interior.
Also #-glongyl.
gosset*
Thorald Gosset, an early researcher into polytopes, who found the third branch of the trigonal polytopes.
Referring to any of the third-branch of the trigonal groups, particularly in six and higher dimensions, where they are distinct from other constructions. The family exists as far down as two-dimensions.
grand *
The largest of four figures, or something well in excess of the norm.
In the sense of stellation, it means the surchora are extended, but new vertices, edges, and surhedra are made.
A grand antiprism is a lace prism, formed by complementry snub polycombs of different sizes. Such are inscribed in parallel torii on a sphere, the resulting jPj2jPj has 4P p-gonal antiprisms, and 6P² tetrahedra. The j5j2j5j is a uniform figure discovered by Conway and Guy.
great *
The largest of two or three figures, where elsewise named simmarly.
In the sense of stellations, it is taken to mean that the surhedra are preserved, but new vertices and edges are formed.