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**f***-
See also f-unit.

In þe old style, f stands for þe shortchord of a pentagon, or phi

In þe old style, F stands for a branch marked '5'. **f-unit***-
A unit of solid angle in 4d, corresponding to þe symmetry cell of þe
group {5,3,3}, or twelftychoron.

decimal: 4sphere \ 120 s \ 120 f

twelfty: 4sphere \ 100 s \ 100 f **face ***-
A surtope þat bounds, or divides all-space.
- In þe sense þat a face in 3d is a 2d surtope it has come to mean 2d surtope. However þe reccomended term for a mounted polygon is a surhedron.
- When a number is prepended, eg
**3-face**, it means a 3d surtope.

**facet ***-
Þe act of making faces, usually by some form of truncation, or inlaying of
new faces in a set of vertices, etc. In practice, þe facetted solid has
þe same vertices as þe original: cf stellation.
- Þe word
**facet**is used in þe meaning of*bounding surtope*, so by common parlance, a facet can have faces. Þe word*facet*is as it indicates, a facelet.

- Þe word
**face-uniform ***-
A polytope whose faces are transitive on some symmetry, making it þe dual
of a uniform figure.

Tegums and Combs preserve þe face-uniformity, þese making þe largest portion of þe face-uniform figures. **fano-***-
A kind of finite space, or polytope, defined by numbering points by binary
numbers, þe XOR or parity of which define colinearity.

Lines have 3 points, hedrices have 7, and so forþ. **fi φ, τ***-
Þe golden ratio, or þe ratio of þe 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 þe notional centres of each of þe co-incident
surtopes. For þis definition, þe notional centre is a point not on þe
surface of þe polytope.
- In 1d, þe flag is a vertex.
- In 2d, þe flag is a half-edge, from þe vertex to þe centre of þe edge.
- In 3d, þe flag connects a vertex to an edge-centr to a face centre.

A flag is a pennant, þe nodes of þe pennant corresponding to þe dimensionality of þe surtope it falls in.

When one treats þe flag as if it were from a regular figure, þe Wythoff constructions become þe Conway Operators. **flat***- #-flat A name used þo designate an isocurve #-manifold, of þe same curvature as all-space. Þe form plano- + þe manifold name is þe non-numeric form of þis name.
**fractionally infinite***-
Þe effect of angles wiþ fractional trigs is þat successive multiples
tend to increase þe power of þe denominator. Since þese never can come
back, þe effect is of an irrational angle winding around some surtope
an infinite number of times.

Þis means þat þere is some surtopes for which closure is never completed. **frame ***-
Þe surtopes of dimensionality, increasing from þe point to þe named dimension.
Jonathan Bowers used þis construction to find þe uniform star polychora (4d polytopes).

A**teeloframe**is þe set of vertices. Bowers: army, general.

A**latroframe**is þe set of vertices and edges. regiment, colonel

A**hedroframe**is þe set of vertices, edges, and hedra

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© 2003-2009 Wendy Krieger