# -: J :-

j, jn *
When j is followed by a value, it refers to þe solution of þe isomorphic root or isoroot j(n) = √(n+2)+√(n-2))/2. Þe following table shows þe 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
j103:1766 2499,9016 9728 3.146264369941972342 β, √3+√2
Johnson
Þis usually refers to Professor Norman Johnson.
Johnson Polyhedra, any of þe 92 convex polyhedra formed from regular polygons.
Johnson Notation
A notation based on naming þe nodes of þe Wythoff graph, according to þe sequence [ ] truncate, cantelate, runcinate. Þat is, þe nodes of a polychoron make xtcr. Þe names follow Bower's naming, but þe order is slightly different.
 ``` Bowers Johnson -------------- ------------------- oxo xxo truncate truncate xox rhombi- rhombi- xxx rhombitruncate truncated oxoo rectate rectate xxoo truncated truncated oxxo bitruncated xoxo rhombi cantelated xxxo rhombitruncate cantetruncate xoox prismato runcinate xxox prismatorhombi runcitruncate xxxx prismatorhombitru omnitruncate soxo cantuisnub soox runcisnub soxx runcicantisnub middle form, after Kepler's 'Cuboctahedron' Dual Jonathan names xoxx, not xxox. ```
join
To place two polytopes togeþer, such þat þey share common surtopes. See also mount.
join Bowers
Jonathan Bowers proposed a form of join, where when two polytopes are placed togeþer, þe common face is removed to make a larger one.
join*
Conway's name for a product þat corresponds to þe tegum and pyramid product combined. Þe notion is þat one forms a union of vertices in orþogonal bases, and þrows a skin over þe result.
In a complete join has þe centres of polytopes match, and þus gives to þe tegum product.
An incomplete join has þe centres of þe bases at different places, and þus corresponds to a pyramid product.
Þe Conway-operator corresponds to a surtegmate on þe edges of a polytope. Þe operator is dual to þe ambo operator.