Here are some things I have collected together:
Using the acronym " STEMP " that stands for Spin, Taper, Extrude, Manifold, Product, we have:
-------------------------------------------------------------------------------------------------------------------------
• mO# - rotate shape M around N-1 plane into N+1, where axis '' # '' is the rotating axis
• m> -taper shape M into N+1
• m| - extrude shape M into N+1
• m(qa) - extrude shape M along surface of shape Q into N+a
• m[q] - cartesian product with shape M and Q, the (m,q)-prism
* Where "a" is number of operators in parentheses
General Shape Families:
-----------------------------
- • |a = N-Cube
• |>a = N-Simplex
• |Oa = N-Sphere
• |Oa>b = N-Sphone
• ||a>b = N-Pyramid**
• |>a|b = N-Pyramid**
• |>a|b>c = N-Pyramid**
• ||aOb = N-Cylinder
• ||aOb>c = N-Cylindrone
• |...[|O] = N-Cylinder
• |...[|>] = N-Trianglinder
* Where "a,b,c" is ≥ 1
** These are just a few of the endless examples as | and > don't commute
0-D
n
* - POINT
-----------------
1-D
X
| - LINE
(O) - HOLLOW CIRCLE / GLOMOLATRIX
----------------------------------
2-D
XY
|O - CIRCLE
|> - TRIANGLE
|| - SQUARE
|(O) - LINE TORUS
|^(O) - ANCHORED LINE TORUS
(OO) - HOLLOW SPHERE / GLOMOHEDRIX
(O)(O) - HOLLOW TORUS / TORIHEDRIX
[(O)(O)] - DUOCYLINDER MARGIN
Complex manifold examples:
(O>) - CONIHEDRIX / HOLLOW CONE
(>>) - TETRAHEDRIX / HOLLOW TETRAHEDRON
----------------------------------------
3-D
XYZ
|OO - SPHERE
|O> - CONE
||O - CYLINDER
|>> - TETRAHEDRON
|>| - TRIANGLE PRISM
||> - SQUARE PYRAMID
||| - CUBE
|O(O) - TORUS
||(O) - SQUARE TORUS
|>(O) - TRIANGLE TORUS
(OOO) - HOLLOW GLOME / GLOMOCHORIX
(OO)(O) - HOLLOW SPHERITORUS
(O)(OO) - HOLLOW TORISPHERE
(O)(O)(O) - HOLLOW DITORUS
|(OO) - LINE TORISPHERE
|(O)(O) - LINE DITORUS
|[(O)(O)] - LINE TIGER
[(O)(O)(O)] - TRIOCYLINDER MARGIN
[(OO)(O)] - CYLSPHERINDER MARGIN
[[(O)(O)](O)] - CYLTORINDER MARGIN
----------------------------------
4-D
XYZW
|OOO - GLOME
|OO> - SPHONE
|OO| - SPHERINDER
|O>> - DICONE
|O>| - CONINDER
|O|O - DUOCYLINDER
||O> - CYLINDRONE
|>>> - PENTACHORON
|>>| - TETRAHEDRINDER
|>|O - CYLTRIANGLINDER
|>|> - TRIANGLE PRISM PYRAMID
|>|| - TRIANGLE DIPRISM
||>> - DIPYRAMID
||>| - PYRAMID PRISM
|||O - CUBINDER
|||> - HEMDODECACHORON / CUBE PYRAMID
|||| - TESSERACT
|>[|>] - DUOTRIANGLINDER
|OO(O) - SPHERITORUS
|O(OO) - TORISPHERE
|O(O)(O) - DITORUS
|O[(O)(O)] - TIGER
|O>(O) - CONE TORUS
||O(O) - CYLINDER TORUS / TORINDER
|>>(O) - TETRAHEDRON TORUS
|>|(O) - TRIANGLE PRISM TORUS
||>(O) - SQUARE PYRAMID TORUS
|||(O) - CUBE TORUS
||(O)(O) - SQUARE DITORUS
|>(O)(O) - TRIANGLE DITORUS
||(OO) - SQUARE TORISPHERE
|>(OO) - TRIANGLE TORISPHERE
(OOOO) - HOLLOW PENTASPHERE / GLOMOTERIX
(OOO)(O) - HOLLOW GLOMITORUS
(O)(OOO) - HOLLOW TORIGLOME
(OO)(OO) - HOLLOW SPHERITORISPHERE
(OO)(O)(O) - HOLLOW SPHERIC DITORUS
(O)(OO)(O) - HOLLOW TORISPHERIC TORUS
(O)(O)(OO) - HOLLOW TORIC TORISPHERE
(O)(O)(O)(O) - HOLLOW TRITORUS
|(OO)(O) - LINE TORISPHERIC TORUS
|(O)(OO) - LINE TORIC TORISPHERE
|(O)(O)(O) - LINE TRITORUS
|(OOO) - LINE TORIGLOME
------------------------------------
5-D
XYZWV
|OOOO - PENTASPHERE
|OOO> - GLONE
|OOO| - GLOMINDER
|OO>> - DISPHONE
|OO>| - SPHONINDER
|OO|O - CYLSPHERINDER
|OO|> - SPHERINDRONE
|OO|| - CUBSPHERINDER
|O>>> - TRICONE
|O>>| - DICONINDER
|O>|O - CYLCONINDER
|O>|> - CONINDER PYRAMID
|O>|| - CONE DIPRISM
||OO> - DUOCYLINDRONE
||O>> - DICYLINDRONE
||O>| - CYLINDRONE PRISM
|>>>> - HEXATERON
|>>>| - PENTACHORINDER
|>>|O - CYLTETRAHEDRINDER
|>>|> - TETRAHEDRINDER PYRAMID
|>>|| - TETRAHEDRON DIPRISM
|>|OO - DUOCYLTRIANGLINDER
|>|O> - CYLTRIANGLINDRONE
|>|O| - CYLTRIANDYINDER
|>|>> - TRIANGLE PRISM DIPYRAMID
|>|>| - TRIANGLIE PRISM PYRAMID PRISM
|>||> - TRIANGLE DIPRISM PYRAMID
|>||| - TRIANGLE TRIPRISM
||>>> - SQUARE-TRIPYRAMID
||>>| - SQUARE DIPYRAMID PRISM
||>|O - CYLHEMOCTAHEDRINDER
||>|> - SQUARE PYRAMID PRISM PYRAMID
||>|| - SQUARE PYRAMID DIPRISM
|O|O| - DUOCYLDYINDER
|||O> - CUBINDRONE
|||>> - CUBE DIPYRAMID
|||>| - CUBE PYRAMID PRISM
||||O - TESSERINDER
||||> - TESSERACT PYRAMID
||||| - PENTERACT
|OO[|>] - SPHENTRIANGLINDER
|O>[|>] - CONTRIANGLINDER
||>[|>] - HEMOCTAHEDROTRIANGLINDER
|>>[|>] - TETRAHEDROTRIANGLINDER
|>[|>]| - DUOTRIANGLINDYINDER
|>[|>]> - DUOTRIANGLINDRIC PYRAMID
|OOO(O) - GLOMITORUS
|O(OOO) - TORIGLOME
|OO(OO) - SPHERITORISPHERE
|OO(O)(O) - SPHERIC DITORUS
|O(OO)(O) - TORISPHERIC TORUS
|O(O)(OO) - TORIC TORISPHERE
|O(O)(O)(O) - TRITORUS
|O[(OO)(O)] - CYLSPHERINTIGROID
|O[[(O)(O)](O)] - CYLTORINTIGROID
|O[(O)(O)](O) - TIGRITORUS
|OO[(O)(O)] - SPHERIC TIGER
|O(O)|O - CYLTORINDER
|O|O(O) - DUOCYLINDRITORUS
Inflated complex manifold:
|O>(O>) - DUOCONTERIX
....and many more toratopes with crosscuts of any other 1,2,3,4D non-toratopes above.
So, I've been working on the construction tables, trying to slim it down a bit. They seem kind of distracting with all of the extra crap. This is my slimmed down version, going downwards now, with the flow of the operators. It's still a mess trying to keep the operators spaced out in the larger shape surtope computations. It's basically a linear progression of surtope lacing from a point.
Here's one of my favorite, of course:
Cylconinder |O>|O = |xOy>z|wOv
* == [ * ]
|x = [ * ]
------------
| == [ *-2 ]
| = [ *-2 ]
Oy = [ (O) ]
---------------
|O = [ *(O) ]
|O == [ *(O) ]
>z === [ * ]
--------------------------
|O> = [ |(O) , |O-* ]
|O> == [ |(O) , |O-* ]
|w === [ |(O) , |O-* ]
-----------------------------------------
|O>| = [ ||(O) , |O|-| , |O>-2 ]
|O>| == [ ||(O) , |O|-| , |O>-2 ]
Ov ===== [ O ....... O ....... (O) ]
-------------------------------------------------
|O>|O = [ ||O(O) , |O|O-|O , |O>(O) ]
-- Philip