-: F :-

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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.

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.

Þe surtegmate is þe gaþering of all flags at a flag-corner.
      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.

forum*

Þe hi.gher.space forum, where much polytope work was done around 2008 to 2012 (twe: 1688 to 1692