# User:Tomruen/Rectified orthoplex

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
t1{4} 4 4
3 Tricross
cuboctahedron
rectified 3-orthoplex
t1{3,4}
12 24 14
4 rectified tetracross
24-cell
rectified 4-orthoplex
t1{3,3,4}
t1{31,1,1}

24 96 96 24
5 Rectified pentacross
rectified 5-orthoplex
t1{33,4}
t1{32,1,1}

40 240 400 240 42
6 rectified hexacross
rectified 6-orthoplex
t1{34,4}
t1{33,1,1}

60 480 1120 1200 576 76
7 rectified heptacross
rectified 7-orthoplex
t1{35,4}
t1{34,1,1}

84 840 2520 3920 3360 1344 142
8 rectified octacross
rectified 8-orthoplex
t1{36,4}
t1{35,1,1}

112 1344 4928 10080 12544 8960 3072 272
9 rectified enneacross
rectified 9-orthoplex
t1{37,4}
t1{36,1,1}

10 rectified decacross
rectified 10-orthoplex
t1{38,4}
t1{37,1,1}