# -: Z :-

Z#*
The set Zn is the span of the chords of a {N}-gon.
Z-span*
The integral span over a set of vectors or numbers.
zero, at*
The result of inversion of at infinity. A isocurve that contains the point at zero is flat in the inversion-geometry. Holes at zero are interior to the solid (but not cavities).
Zero-Curvature*
An isocurve having Euclidean geometry. Unlike other curves, this retains the same curvature on dilation.
Constructions in horo- are preferred
Zenith Sphere *
The form of lattitude in four dimensions is different to three dimensions. In four dimensions, the nature of rotation is to equalise, so that each mode of rotation has the same energy: a clifford-style rotation comes of it.
Lattitude is derived by dividing the surface of a rotating sphere by by its rotation. In three dimensions, this yields the gimbus that supports the globe. It runs from +90 to -90, where higher dimensions make colder temperatures, and the N and S make two season-zones.
In four dimensions, this arc is bent into a circle of half-size, running from 0 at one pole to 90 at the other. This is rotated so that it becomes a sphere, where the lattitudes correspond to S = 0 deg = hot, and N = 90 = cold, while the longitudes correspond to separate seasons. One has all seasons at any given time.
The stars follow a line of longitude, which is perpendicular to this sphere. So their whole motion is on a circle represented by a point on a zenith sphere. A point on the surface at this same point would be at places where the star reaches the zenith.
The sun is supposed to follow a non-clifford parallel, which means that its zenith points lie against a line of say 23.5 deg, travelling on this circle once a year. As it crosses the particular line of "longitude", it makes the effect of mid-summer's day. The effect is that the sun is rising nearest a given point at this time, and thus more light falls on a ground, making it warmer. Actual seasons lag as the do here.
zettix
A seven-dimensional manifold, from which one makes zettons. See hedrix for details.
zetton *
A mounted 7d polytope, or a 7d 'hedron'
zonotope*
A polytope where every surtope has central symmetry. Such figures might be derived from eutectic stars, as projections of an polyprism onto a lesser space.
For example, the rhombic dodecahedron is a zonotope, because its surhedra all have central symmetry. It can be viewed as a projection of the tesseract or tetraprism onto a three-dimensional space.
The pentagonal dodecahedron is not a zonotope, because pentagons do not have centre of symmetry.
ZZ*
The sum of sets Z#, or the span of all chords of all polygons.