-: F :-

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See also f-unit.
In the old style, f stands for the shortchord of a pentagon, or phi
In the old style, F stands for a branch marked '5'.

f-unit *

A unit of solid angle in 4d, corresponding to the symmetry cell of the group {5,3,3}, or twelftychoron.
decimal: 4sphere \ 120 s \ 120 f
twelfty: 4sphere \ 100 s \ 100 f

face *

A surtope that bounds, or divides all-space.

In the sense that a face in 3d is a 2d surtope it has come to mean 2d surtope. However the reccomended term for a mounted polygon is a surhedron.
When a number is prepended, eg 3-face, it means a 3d surtope.

facet *

The act of making faces, usually by some form of truncation, or inlaying of new faces in a set of vertices, etc. In practice, the facetted solid has the same vertices as the original: cf stellation.

The word facet is used in the meaning of bounding surtope, so by common parlance, a facet can have faces. The word facet is as it indicates, a facelet.

face-uniform *

A polytope whose faces are transitive on some symmetry, making it the dual of a uniform figure.
Tegums and Combs preserve the face-uniformity, these making the largest portion of the face-uniform figures.

fano-*

A kind of finite space, or polytope, defined by numbering points by binary numbers, the XOR or parity of which define colinearity.
Lines have 3 points, hedrices have 7, and so forth.

fi φ, τ *

The golden ratio, or the ratio of the diagonal of a pentagon to its side.
φ = τ = (√5+1)/2 ; also φ² = φ+1
(twe: 1:7419 8287,V8V3 43E0,7999 V161,9009 9993,46V7 V807)
(dec: 1.618033988749894848204586834365638117720)

flag *

A simplex, formed by the notional centres of each of the co-incident surtopes. For this definition, the notional centre is a point not on the surface of the polytope.

In 1d, the flag is a vertex.
In 2d, the flag is a half-edge, from the vertex to the centre of the edge.
In 3d, the flag connects a vertex to an edge-centr to a face centre.

The surtegmate is the gathering of all flags at a flag-corner.
A flag is a pennant, the nodes of the pennant corresponding to the dimensionality of the surtope it falls in.
When one treats the flag as if it were from a regular figure, the Wythoff constructions become the Conway Operators.

flat *

#-flat A name used tho designate an isocurve #-manifold, of the same curvature as all-space. The form plano- + the manifold name is the non-numeric form of this name.

fractionally infinite *

The effect of angles with fractional trigs is that successive multiples tend to increase the power of the denominator. Since these never can come back, the effect is of an irrational angle winding around some surtope an infinite number of times.
This means that there is some surtopes for which closure is never completed.

frame *

The surtopes of dimensionality, increasing from the point to the named dimension. Jonathan Bowers used this construction to find the uniform star polychora (4d polytopes).
A teeloframe is the set of vertices. Bowers: army, general.
A latroframe is the set of vertices and edges. regiment, colonel
A hedroframe is the set of vertices, edges, and hedra

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