| Site Map | Polytopes | Dynkin Diagrams | Vertex Figures, etc. | Incidence Matrices | Index |
This page just aims for a short reference. Detailed explanations can be found here.
| Link symbols | Example | |
|
3 4 5 5/2 etc., in general: n/d | subdivisor of π used as angle between the adjacent mirrors (node symbols) | x4/3x3o |
| 2 |
links marked 2 are usually omitted (left blank) denoting the polytope being the prism-product
of the polytopes of the unconnected component-symbols in cases of snubs they are re-introduced in order to show that the semiation runs across the thus connected components, instead of being a prism-product of (separate) snub components |
x x4o
s2s3s |
| - | sometimes introduced on both sides of a link-mark to separate those more clearly from the node symbols | x-n/d-o |
| Node symbols | Example | |
| o |
unringed (real) node seed-point of construction lies on that mirror | o3o5x |
| x |
ringed (real) node seed-point of construction lies off that mirror, thus demarking (usually) a unit edge | |
|
x(2) = o x(3) = x x(4) = q x(5) = f x(5/2) = v x(6) = h x(∞) = x(6,3) = u x(8,3) = w in general: x(n/d,m) uppercase letters |
edge of length 0 (or no edge at all) edge of length 1 edge of length sqrt(2) = 1.414214 edge of length (1+sqrt(5))/2 = 1.618034 edge of length (sqrt(5)-1)/2 = 0.618034 edge of length sqrt(3) = 1.732051 edge of length 2 edge of length 1+sqrt(2) = 2.414214 edge of length sin(π md/n)/sin(π d/n) occuring as chord of a regular {n/d}-gon, connecting a vertex with its m-th successor (if m is omitted as argument, then m=2 is understood) other edge lengths, to be defined within a local context ad hoc |
u3x4o F=ff=x+f |
|
*a *b *c etc. | virtual nodes, introduced just for linearization of the symbol, refferring to the re-visitation of the first (a-th), second (b-th), third (c-th), etc. real node position (where counting starts at the left of the symbol) |
x3o3o *b3o3o x3o3o3*a |
| s | snub node | s5/2s5s |
| β | holosnub node | β3o3x |
| Lacings | Example | |
| &#. | Lace-prisms (or more general lace-simplices) use vertices arranged in several "layers" with some common symmetry. These cross-sections are linked by lacing edges of length ".", i.e. corresponding to that node-symbol; usually "&#x". That lacing mark is attached to the right end of the double load (prisms) resp. multiple load (count of mutually connected layers ≥ 2: simplices) of the symmetry-graph. | xx3ox&#x |
| &#.t | Lace-tower, i.e. a stack of lace-prisms | xux3oox&#xt |
| &#.r | Lace-rings, i.e. the body encompassed by a circuit of lace-prisms (not the thus described torus) | xxoo&#xr |
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