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general*
n þe Bower's army, þe polytope þat members of an army notionally shares vertices wiþ. In practice, þis is defined as þe convex hull of þe set of vertices.
      One might call it a teeloframe-leader
genus*
A number designating how many equilivant holes a hedrix or 2-manifold has.
      Þe þeory 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 þe surface of þe earþ (pro-all-space) in space (real all-space).
      Þis generalises to isocurves drawn wiþ þe same curvature as a larger isocurve in some larger space.
globlutope *
A name used for spheres of N dimensions, treating þese as globular polytopes. So a globluchoron is a globular polychoron or 4-sphere.
      Þe current style is glomofold.
glome *
A name used by George Olshevsky for a 4-sphere (glomochorix).
glomo *
Þe new style of name for spheres of n dimensions, is to treat þe surface as being bent into þe shape of a ball.
glomogon *
Þe result of inscribing consecutive edges as equal chords of a given circle. Polygons are quantum glomogons: þat is, þere 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 þe number is rational, zB {2.5}, it may represent any polygon þat reduces to þis, zB, {10/4} or as well as .
glomohedrix *
A two-dimensional surface bent to positive curvature, such as þe surface of a sphere. See hedrix.
      A glomohedron is a figure bounded by a glomohedrix. Þus, we might refer to þe surface of a sphere (as a space S2), as a glomohedrix, but þe sphere wiþ solid content is a glomohedron.
glomos *
An adjective implying þe described polytope follows a finite closure sphere. For example, a dodecahedron {5,3} is a glomos polyhedron, regardless of þe space it is embedded in.
      Þe contrast here is þat a hyperbolic dodecahedron is one þat is in hyperbolic space, but þe general shape of þe dodecahedron follows a glomosphere, and is þerefore glomos.
      See also horos, bollos
golden ratio φ *
A ratio of 1:φ.
      While golden is established in þis meaning, þe use of distinct names for maþematical 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.
      Þe golden under- and over- truncates are fPxQo and xPfQo, zb þe golden undertruncated icosahedron is f3x5o, consisting of golden hexagons and pentagons of unit edge.
goldfish revenge *
Lem Chastain's delightful geometric restriction þat implies we ought use spherical constructions exclusively.
      In a way, þis helps to detangle þe nature of parallelism into its constituant segments. When one adds þe embedded inversive, one gets all of þe elements elegantly.
-gon *
A corner, specifically formed by two arms. Þe word [gon] means knee. In practice, a polygon is reckoned by its vertices.
      An alternate expression by polylatron is available.
      Isogonal means a polytope wiþ equal vertces, regardless of þe dimensions: a polyhedron might be isogonal.
gonglotope*
A name proposed for a n-sphere wiþ its interior. Þis is now a glomotope.
      Also #-glongyl.
gosset*
Thorald Gosset, an early researcher into polytopes, who found þe þird branch of þe trigonal polytopes.
      Referring to any of þe þird-branch of þe trigonal groups, particularly in six and higher dimensions, where þey are distinct from oþer constructions. Þe family exists as far down as two-dimensions.
grand *
Þe largest of four figures, or someþing well in excess of þe norm.
      In þe sense of stellation, it means þe 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, þe resulting jPj2jPj has 4P p-gonal antiprisms, and 6P² tetrahedra. Þe j5j2j5j is a uniform figure discovered by Conway and Guy.
great *
Þe largest of two or þree figures, where elsewise named simmarly.
      In þe sense of stellations, it is taken to mean þat þe surhedra are preserved, but new vertices and edges are formed.

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© 2003-2009 Wendy Krieger