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**j, jn ***-
When j is followed by a value, it refers to the solution of the isomorphic
root or isoroot j(n) = √(n+2)+√(n-2))/2. The following table
shows the more important geometric isoroots.
- twelfty decimal symbol j3 1:7419 8287,V8V3 43E0 1.618033988749894848 φ, τ j4 1:E198 7978,8151 V4E3 1.931851652578136573 ω j6 2:4984 8104,3529 0779 2.414213562373095048 α j10 3:1766 2499,9016 9728 3.146264369941972342 β, √3+√2 **Johnson**-
This usually refers to Professor Norman Johnson.

*Johnson Polyhedra*, any of the 92 convex polyhedra formed from regular polygons. **Johnson Notation**-
A notation based on naming the nodes of the Wythoff graph, according to the
sequence
`[ ] truncate, cantelate, runcinate`. That is, the nodes of a polychoron make xtcr. The names follow Bower's naming, but the order is slightly different.Bowers Johnson -------------- ------------------- oxo <meso> <meso> xxo truncate truncate xox rhombi- rhombi- xxx rhombitruncate truncated <meso> oxoo rectate rectate xxoo truncated truncated oxxo <meso> bitruncated xoxo rhombi cantelated xxxo rhombitruncate cantetruncate xoox prismato <meso> runcinate xxox prismatorhombi <d> runcitruncate xxxx prismatorhombitru omnitruncate soxo cantuisnub soox runcisnub soxx runcicantisnub <meso> middle form, after Kepler's 'Cuboctahedron' <d> Dual Jonathan names xoxx, not xxox.

**join**- To place two polytopes together, such that they share common surtopes. See also mount.
**join***Bowers*- Jonathan Bowers proposed a form of join, where when two polytopes are placed together, the common face is removed to make a larger one.
**join***-
Conway's name for a product that corresponds to the tegum and pyramid product
combined. The notion is that one forms a union of vertices in orthogonal
bases, and throws a skin over the result.

In a**complete**join has the centres of polytopes match, and thus gives to the tegum product.

An**incomplete**join has the centres of the bases at different places, and thus corresponds to a pyramid product.

The Conway-operator corresponds to a surtegmate on the edges of a polytope. The operator is dual to the ambo operator.

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© 2003-2009 Wendy Krieger