-: N :-

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The dual of the Polytope Army, members common to the same navy unit share the same surtope, and those of higher dimensions. Because the lesser dimensions are relocated, the sharing of surtopes implies only that there is one in the corresponding flats.

The navy units are closely allied to the process of stellation.

    Unit         group     leader         Stellation        name
    face-navy     fleet     admiral   |   edge-navy         stellated
    margin-navy   ship      commodore |   surhedron-navy    great
    2margin-navy  boat      coxwain   |   surchoron-navy    grand

Navy units form sets etc as does the army units. However, increasing the surtope of the navy unit makes the grouping coarser, not finer. So while an vertex-army contains several edge-armies, the edge-navy contains several vertex-navies. See also Army

The second-series name for an vertex: see sesquitope
Coxeter's name for any spheric tiling that in parabolic space becomes flat. Typically, these involve a 2 in the Schlafli symbol, and marks on only one side of it, eg {;2,p} = hosohedra, {p,2} = dihedra.

A noid is solid if the sphere that the tiling covers is solid.

The designation given to a uniform figure not constructable by Wythoff's mirror-edge construction on a simplex-mirror group. There are not many of these outside of the hyperbolic aperihedra.
    Name            Description             Discoverer
    snub {;P;Q;R:}  vf (3,P,3,Q,3,R)        ?
    s{;3;4,3}       snub 24-chora           Wythoff, Stott
    j5j2j5j         grand antiprism         John Conway & Richard Guy
    s{;3;4,3,3}     snub {3,4,3,3}          ?
    t-pr            prismatoreflects*       ?
    borromeal       {p}-borromochora*       Charlie Gunn
    (four cases)    octacubics*             Wendy Krieger
    pt{3,5,3}       partialtruncate*        Wendy Krieger
See also snub(Coxeter) and snub(Wythoff)
nullitope *
The notional -1 edge, that arises as the dual of the solid substance of a polytope. This is normally residing at infinity, and gives rise to "spiritual" connections because of this. It is part of the surtope equation.
nulloid *
A calculation fiction introduced to simplify a number of calculations. The surtope is reckoned as having d-1, and residing at a vast distance.
      In the process of duals, this is the orthosurtope of the bulk.
      A single nulloid is reckoned in the tegum and pyramid products.

Gloss:Home Intro A B C D E F G H I J K L M N O P Q R S T Th U V W X Y Z

© 2003-2009 Wendy Krieger