Here's something I put together last couple of days. It's a graphic of toratope notation, along with the equation, and some other stuff.
R^2 to R^4 : http://i.imgur.com/VubABFd.png
R^5 : http://i.imgur.com/wTMGsYV.png
ICN5D wrote:Do the CoexeterDynkin symbols have a tree graph associated with them?
xPoQo : 3D body

xPo . : 2D faces

x . . : 1D edges

. . . : 0D vertices

empty :1D nulloid
oPxQo : 3D body
/ \
oPx . . xQo : 2D faces
\ /
. x . : 1D edges

. . . : 0D vertices

empty :1D nulloid
xPxQo : 3D body
/ \
xPx . . xQo : 2D faces
/ \ /
x . . . x . : 1D edges
\ /
. . . : 0D vertices

empty :1D nulloid
xPoQx : 3D body
/  \
xPo . x . x . oQx : 2D faces
\ / \ /
x . . . . x : 1D edges
\ /
. . . : 0D vertices

empty :1D nulloid
xPxQx : 3D body
/  \
xPx . x . x . xQx : 2D faces
 X X 
x . . . x . . . x : 1D edges
\  /
. . . : 0D vertices

empty :1D nulloid
wendy wrote:The hasse diagram of any polytope that has a dual, is simply the antitegum of the polytope (which is the same as the dual), ie
For a wythoffpolytope, it's a matter of replacing o, x with oo, xm, and then put &#mt at the end. This is of course, to suppose a point expanding into a polytope as a pyramid peak in one direction, and from inside this pyramid peak, a second of the dual expanding. If ye look at the cube, you can colour three faces around a point red, and the opposite three blue. This gives an expansion of triangles from the red vertex, until the triangles meet the blue bits and the section becomes a hexagon (truncated triangle), and then a point (rectified triangle).
Users browsing this forum: No registered users and 1 guest