So, yeah, 5D is cool and all, but I'm interested in some of the bigger monsters out there. I don't expect the wiki to detail ALL the shapes, that would be a very long process. At least, not until regular patterns can be extrapolated and plugged into a computer program. Then the sky's the limit!
The bi-cyltrianglinder prism , square{cyltrianglinder,cyltrianglinder}, an eight dimensional monster unveiled
Also made by:
* cube{triangle-prism,cone,circle}
Cartesian Product: |>|O(|>|O) , |>|(|O>)(|O)
C{ |>|Oxyzw , (|>|Ovuts) } == |>|O(|>|O)
-----------------------------------------
C{ |>(O) , |>|O }xy == [ |>||>O(O) ]xy
C{ ||O-2 , |>|O }z == [ |>|||OO-2 ]z
C{ ||O-|O , |>|O }w == [ |>|||OO-|>||OO ]w
C{ |>|O , |>(O) }vu == [ |>||>O(O) ]vu
C{ |>|O , ||O-2 }t == [ |>|||OO-2 ]t
C{ |>|O , ||O-|O }s == [ |>|||OO-|>||OO ]s
The features that we can derive out of this are:
* 6 flat |>|||OO side panels
--- In 2 groups of 3, along perpendicular planes zw and ts
* 2 |>||>0 torii connecting curved surfaces of flat panels
* 6 triangular attachments, at a |>||OO for a vertex
* 2 curved rolling surfaces, bisected by planes xy and vu
* Rolls along 2 perpendicular directions
* A |>||>O for a contact patch resting on a 7-plane
* Net of 6 |>|||OO , bound to 2 |>||>O prisms
* Duocylinder-like rolling capabilities combined with 2 bisecting perpendicular triangles. So, it could be called, in a ways, a duocylindric duotrianglinder.
Cross sections are:
* A |>|||OO scaling down to a |>||OO through a flat side
* A |>||>O expanding into a |>||>O-prism, then collapsing back into a |>||>O through either rolling surface
Hypervolumes:
* 7-surface Bulk: 6(|>|||OO ) + 2(|>||>O(O)) 7-volumes
* 8-surface Bulk: yeah right, that way beyond me!