User:Tomruen/Rectified orthoplex

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Quick rebuild from orthoplex.

The class of rectified orthoplexes are special for having a circumradius equal to their edge-length. Thus they all can be used as vertex figures for uniform tessellations. Tom Ruen (talk) 21:54, 1 June 2010 (UTC)

Cross-polytope elements
n Name(s)
Graph
Graph
2n-gon
Schläfli Coxeter-Dynkin
diagrams
Vertices Edges Faces Cells 4-faces 5-faces 6-faces 7-faces 8-faces 9-faces
2 Bicross
square
rectified 2-orthoplex
Cross graph 2.png t1{4} CDel node 1.pngCDel 4.pngCDel node.png 4 4                
3 Tricross
cuboctahedron
rectified 3-orthoplex
Rectified 3-cube.png t1{3,4} CDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
12 24 14              
4 rectified tetracross
24-cell
rectified 4-orthoplex
Rectified 16-cell petrie.png t1{3,3,4}
t1{31,1,1}
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node.pngCDel 3.pngCDel node 1.pngCDel split1.pngCDel nodes.png
24 96 96 24            
5 Rectified pentacross
rectified 5-orthoplex
Rectified pentacross.png t1{33,4}
t1{32,1,1}
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes.png
40 240 400 240 42          
6 rectified hexacross
rectified 6-orthoplex
Rectified hexacross.png t1{34,4}
t1{33,1,1}
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes.png
60 480 1120 1200 576 76        
7 rectified heptacross
rectified 7-orthoplex
Rectified heptacross.png t1{35,4}
t1{34,1,1}
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes.png
84 840 2520 3920 3360 1344 142      
8 rectified octacross
rectified 8-orthoplex
Rectified octacross.png t1{36,4}
t1{35,1,1}
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes.png
112 1344 4928 10080 12544 8960 3072 272    
9 rectified enneacross
rectified 9-orthoplex
Rectified enneacross.png t1{37,4}
t1{36,1,1}
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes.png
 
10 rectified decacross
rectified 10-orthoplex
Rectified decacross.png t1{38,4}
t1{37,1,1}
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes.png