rox

Acronym rox

Name rectified hexacosachoron

Cross sections

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Circumradius sqrt[5+2 sqrt(5)] = 3.077684

Vertex figure

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Vertex layers

Layer	Symmetry	Subsymmetries
	`o3o3o5o`	`o3o3o .`	`o3o . o`	`o . o5o`	`. o3o5o`
1	`o3x3o5o`	`o3x3o .` oct first	`o3x . o` {3} first	`o . o5o` vertex first	`. x3o5o` ike first
2		`x3o3f .`	`x3o . f`	`x . x5o` vertex figure	`. o3x5o`
3		`x3f3o .`	`x3f . x`	`o . o5f`	`. x3o5x`
4a		`F3o3x .`	`o3f . F`	`F . o5x`	`. F3o5o`
4b		`o3f3f .`	`o3f . F`	`F . o5x`	`. F3o5o`
5a		`f3o3F .`	`F3o . f`	`f . x5x`	`. o3f5o`
5b		`f3o3F .`	`F3o . f`	`W . o5o`	`. o3f5o`
6a		`f3f3x .`	`o3V . o`	`o . x5f`	`. f3o5x`
6b			`F3x . o`	`V . f5o`
6c			`f3o . V`	`V . f5o`
7a		`o3x3V .`	`f3f . F`	`x . F5o`	`. o3x5x`
7b		`V3x3o .`	`f3f . F`	`X . o5x`	`. o3x5x`
8a		`o3F3f .`	`f3F . x`	`f . o5F`	`. f3x5o`
8b		`o3F3f .`	`o3x . X`	`f . o5F`	`. f3x5o`
9a		`f3x3F .`	`V3x . f`	`F . f5x`	`. V3o5o`
9b		`x3V3o .`	`o3F . W`	`F . f5x`	`. x3o5f`
10a		`F3f3x .`	`X3o . o`	`x . f5f`	`. f3x5o`
10b		`F3f3x .`	`X3o . o`	`X . x5x`	`. f3x5o`
11a		`x3o3X .`	`o3X . x`	`o . V5o`	`. o3x5x`
11b		`X3o3x .`	`f3x . X`	`V . o5F`
11c		`X3o3x .`	`f3x . X`	`Y . x5o`
12a		`V3o3F .`	`x3V . F`	`f . o5V`	`. f3o5x`
12b		`x3F3f .`	`x3V . F`	`W . F5o`	`. f3o5x`
13a		`o3X3o .`	`f3W . o`	`F . f5f`	`. o3f5o`
13b			`F3f . V`	`Z . o5o`
13c			`x3o . Y`	`Z . o5o`
14a		`f3x3V .`	`F3F . f`	`o . x5F`	`. F3o5o`
14b		`W3f3o .`	`F3F . f`	`Y . o5f`	`. F3o5o`
15a		`o3x3X .`	`X3o . F`	`x . F5x`	`. x3o5x`
15b		`F3f3f .`	`X3o . F`	`X . x5f`	`. x3o5x`
16a		`o3F3F .`	`X3x . x`	`F . V5o`	`. o3x5o`
16b		`X3o3f .`	`V3o . X`	`Z . x5o`
16c		`X3o3f .`	`x3F . X`	`Z . x5o`
17		`x3V3x .`	`x3X . f`	`f . x5F`	`. x3o5o` opposite ike
18a		`F3F3o .`	`V3F . o`	`X . F5o`
18b		`f3o3X .`	`o3X . V`
18c		`f3o3X .`	`f3x . Y`
19a		`X3x3o .`	`W3f . F`	`o . F5F`
19b		`f3f3F .`	`o3x . Z`	`V . f5f`
19c		`f3f3F .`	`o3x . Z`	`Y . x5x`
20a		`V3x3f .`	`F3f . X`	`X . o5F`
20b		`o3f3W .`	`F3f . X`	`X . o5F`
21a		`o3X3o .`	`f3X . o`	`f . F5x`
21b			`Y3o . o`
21c			`o3F . Y`
22a		`F3o3V .`	`F3V . f`	`F . o5V`
22b		`f3F3x .`	`X3o . W`	`Z . o5x`
23a		`X3o3x .`	`X3f . x`	`x . x5F`
23b		`x3o3X .`	`o3Y . x`	`X . f5x`
23c		`x3o3X .`	`x3V . X`	`X . f5x`
24a		`x3f3F .`	`x3X . F`	`o . F5x`
24b		`x3f3F .`	`f3o . Z`	`Y . f5o`
25a		`F3x3f .`	`F3F . V`	`F . f5f`
25b		`o3V3x .`	`f3f . Y`	`Z . o5o`
26a		`f3F3o .`	`X3x . F`	`f . V5o`
26b		`f3F3o .`	`o3f . Z`	`W . o5F`
27a		`V3x3o .`	`f3X . x`	`o . o5V`
27b		`o3x3V .`	`Y3o . x`	`V . F5o`
27c		`o3x3V .`	`V3x . X`	`Y . o5x`
28a		`x3f3f .`	`V3F . f`	`x . f5f`
28b		`x3f3f .`	`o3X . W`	`X . x5x`
29a		`F3o3f .`	`X3f . o`	`F . x5f`
29b			`o3Y . o`
29c			`F3o . Y`
30a	`x3o3F .`	`f3F . X`	`f . F5o`
30b	`f3f3o .`	`f3F . X`	`f . F5o`
31a	`o3f3x .`	`f3W . F`	`x . o5F`
31b	`o3f3x .`	`x3o . Z`	`X . x5o`
32a	`f3o3x .`	`F3V . o`	`o . f5x`
32b		`X3o . V`	`V . o5f`
32c		`x3f . Y`	`V . o5f`
33a	`o3x3o .` opposite oct	`X3x . f`	`f . x5x`
33b	`o3x3o .` opposite oct	`X3x . f`	`W . o5o`
34a		`x3X . x`	`F . x5o`
34b		`o3V . X`
34c		`F3x . X`
35		`o3X . F`	`o . f5o`
36		`F3F . f`	`x . o5x`
37a		`W3f . o`	`o . o5o` opposite vertex
37b		`f3F . V`
37c		`o3x . Y`
38		`V3x . F`
39a		`X3o . x`
39b		`x3f . X`
40		`o3X . o`
41a		`x3V . f`
41b		`F3o . W`
42a		`F3f . x`
42b		`x3o . X`
43		`f3f . F`
44a		`V3o . o`
44b		`x3F . o`
44c		`o3f . V`
45		`o3F . f`
46		`f3o . F`
47		`f3x . x`
48		`o3x . f`
49		`x3o . o` opposite {3}

(F=ff=x+f=2x+v, V=F+v=2f=2x+2v, W=F+x=3x+v, X=fff=W+v=3x+2v, U=3f=3x+3v, Y=X+x=4x+2v=2F, Z=Y+v=4x+3v, T=FF=5x+3v)

Lace city
in approx. ASCII-art

©

                                            o5o                                            
                                    x5o             x5o                                    
                                            o5f                                            
                        o5x                                     o5x                        
                o5o             x5x                     x5x             o5o                
                                                                                           
                    f5o                     x5f                     f5o                    		F=ff=x+f=2x+v, 
            o5x                     F5o             F5o                     o5x            		V=F+v=2f=2x+2v
                                o5F                     o5F                                
                        f5x                                     f5x                        
                                                                                           
            x5x                     f5f             f5f                     x5x            
    x5o             o5F                     V5o                     o5F             x5o    
                                                                                           
                F5o             o5V                     o5V             F5o                
o5o                     f5f                                     f5f                     o5o
    o5f                                     x5F                                     o5f    
            x5f                     F5x             F5x                     x5f            
                                                                                           
x5o                     V5o                                     V5o                     x5o
                                x5F                     x5F                                
            F5o                                                             F5o            
    x5x             f5f                     F5F                     f5f             x5x    
            o5F                                                             o5F            
                                F5x                     F5x                                
o5x                     o5V                                     o5V                     o5x
                                                                                           
            f5x                     x5F             x5F                     f5x            
    f5o                                     F5x                                     f5o    
o5o                     f5f                                     f5f                     o5o
                o5F             V5o                     V5o             o5F                
                                                                                           
    o5x             F5o                     o5V                     F5o             o5x    
            x5x                     f5f             f5f                     x5x            
                                                                                           
                        x5f                                     x5f                        
                                F5o                     F5o                                
            x5o                     o5F             o5F                     x5o            
                    o5f                     f5x                     o5f                    
                                                                                           
                o5o             x5x                     x5x             o5o                
                        x5o                                     x5o                        
                                            f5o                                            
                                    o5x             o5x                                    
                                            o5o

©

                        x3o   o3f f3o   o3x                        
                                                                   
                o3x   x3f F3o   f3f   o3F f3x   x3o                
                                                                   		F=ff=x+f=2x+v, 
                                                                   		V=F+v=2f=2x+2v, 
         x3o x3f  oF3Vx  f3F V3x   x3V F3f  Vx3oF  f3x o3x         		W=F+x=3x+v, 
                                                                   		X=fff=W+v=3x+2v, 
           F3o             o3X       X3o             o3F           		Y=X+x=4x+2v=2F
      o3f       f3F   X3o       F3F       o3X   F3f       f3o      		_DONE_
                                                                   
    f3o f3f   V3x o3X   f3W   X3x x3X   W3f   X3o x3V   f3f o3f    
                                                                   
                                                                   
 o3x o3F   x3V   F3F X3x   V3F       F3V   x3X F3F   V3x   F3o x3o 
                                                                   
   f3x   F3f X3o   x3X      fY3Xo Xo3fY      X3x   o3X f3F   x3f   
                                                                   
                                                                   
x3o  Vx3oF  o3X W3f   F3V #           #   V3F   f3W X3o  oF3Vx  o3x
                        (Xo3fY)     (fY3Xo)                        
                                                                   
   f3x   F3f X3o   x3X      fY3Xo Xo3fY      X3x   o3X f3F   x3f   
                                                                   
 o3x o3F   x3V   F3F X3x   V3F       F3V   x3X F3F   V3x   F3o x3o 
                                                                   
                                                                   
    f3o f3f   V3x o3X   f3W   X3x x3X   W3f   X3o x3V   f3f o3f    
                                                                   
      o3f       f3F   X3o       F3F       o3X   F3f       f3o      
           F3o             o3X       X3o             o3F           
                                                                   
         x3o x3f  oF3Vx  f3F V3x   x3V F3f  Vx3oF  f3x o3x         
                                                                   
                                                                   
                o3x   x3f F3o   f3f   o3F f3x   x3o                
                                                                   
                        x3o   o3f f3o   o3x

General of army (is itself convex)

Colonel of regiment

(is itself locally convex – uniform polychoral members:

by cells:	gad	id	ike	oct	pip	saddid	sird	srid	tid
rofix	120	120	0	0	0	0	0	0	0
ipixady	120	0	0	600	0	120	0	0	0
nipixady	120	0	0	600	0	0	0	120	0
sophi	120	0	0	0	720	0	0	0	0
frox	0	120	0	0	720	0	0	0	0
rox	0	0	120	600	0	0	0	0	0
sprapivady	0	0	120	0	0	0	0	0	120
lifpipixhi	0	0	0	600	720	120	0	0	0
rixhi	0	0	0	600	0	0	0	0	120
sriphi	0	0	0	0	0	0	120	0	0

& others)

Confer

Grünbaumian relatives:: rox+720pip 2rox 2rox+1440{5}+2400{3}
segmentochora:: ike || id id || srid pippy
related CRFs:: spidrox

External
links

As abstract polytope rox is isomorphic to raggix, thereby replacing pip vertex figures by stip ones, resp. by replacing ike by gike.

Incidence matrix according to Dynkin symbol

o3x3o5o

. . . . | 720 ♦   10 |    5   10 |   5   2
--------+-----+------+-----------+--------
. x . . |   2 | 3600 |    1    2 |   2   1
--------+-----+------+-----------+--------
o3x . . |   3 |    3 | 1200    * |   2   0
. x3o . |   3 |    3 |    * 2400 |   1   1
--------+-----+------+-----------+--------
o3x3o . ♦   6 |   12 |    4    4 | 600   *
. x3o5o ♦  12 |   30 |    0   20 |   * 120

o3x3o5/4o

. . .   . | 720 ♦   10 |    5   10 |   5   2
----------+-----+------+-----------+--------
. x .   . |   2 | 3600 |    1    2 |   2   1
----------+-----+------+-----------+--------
o3x .   . |   3 |    3 | 1200    * |   2   0
. x3o   . |   3 |    3 |    * 2400 |   1   1
----------+-----+------+-----------+--------
o3x3o   . ♦   6 |   12 |    4    4 | 600   *
. x3o5/4o ♦  12 |   30 |    0   20 |   * 120

o3x3/2o5o

. .   . . | 720 ♦   10 |    5   10 |   5   2
----------+-----+------+-----------+--------
. x   . . |   2 | 3600 |    1    2 |   2   1
----------+-----+------+-----------+--------
o3x   . . |   3 |    3 | 1200    * |   2   0
. x3/2o . |   3 |    3 |    * 2400 |   1   1
----------+-----+------+-----------+--------
o3x3/2o . ♦   6 |   12 |    4    4 | 600   *
. x3/2o5o ♦  12 |   30 |    0   20 |   * 120

o3x3/2o5/4o

. .   .   . | 720 ♦   10 |    5   10 |   5   2
------------+-----+------+-----------+--------
. x   .   . |   2 | 3600 |    1    2 |   2   1
------------+-----+------+-----------+--------
o3x   .   . |   3 |    3 | 1200    * |   2   0
. x3/2o   . |   3 |    3 |    * 2400 |   1   1
------------+-----+------+-----------+--------
o3x3/2o   . ♦   6 |   12 |    4    4 | 600   *
. x3/2o5/4o ♦  12 |   30 |    0   20 |   * 120

o3/2x3o5o

.   . . . | 720 ♦   10 |    5   10 |   5   2
----------+-----+------+-----------+--------
.   x . . |   2 | 3600 |    1    2 |   2   1
----------+-----+------+-----------+--------
o3/2x . . |   3 |    3 | 1200    * |   2   0
.   x3o . |   3 |    3 |    * 2400 |   1   1
----------+-----+------+-----------+--------
o3/2x3o . ♦   6 |   12 |    4    4 | 600   *
.   x3o5o ♦  12 |   30 |    0   20 |   * 120

o3/2x3o5/4o

.   . .   . | 720 ♦   10 |    5   10 |   5   2
------------+-----+------+-----------+--------
.   x .   . |   2 | 3600 |    1    2 |   2   1
------------+-----+------+-----------+--------
o3/2x .   . |   3 |    3 | 1200    * |   2   0
.   x3o   . |   3 |    3 |    * 2400 |   1   1
------------+-----+------+-----------+--------
o3/2x3o   . ♦   6 |   12 |    4    4 | 600   *
.   x3o5/4o ♦  12 |   30 |    0   20 |   * 120

o3/2x3/2o5o

.   .   . . | 720 ♦   10 |    5   10 |   5   2
------------+-----+------+-----------+--------
.   x   . . |   2 | 3600 |    1    2 |   2   1
------------+-----+------+-----------+--------
o3/2x   . . |   3 |    3 | 1200    * |   2   0
.   x3/2o . |   3 |    3 |    * 2400 |   1   1
------------+-----+------+-----------+--------
o3/2x3/2o . ♦   6 |   12 |    4    4 | 600   *
.   x3/2o5o ♦  12 |   30 |    0   20 |   * 120

o3/2x3/2o5/4o

.   .   .   . | 720 ♦   10 |    5   10 |   5   2
--------------+-----+------+-----------+--------
.   x   .   . |   2 | 3600 |    1    2 |   2   1
--------------+-----+------+-----------+--------
o3/2x   .   . |   3 |    3 | 1200    * |   2   0
.   x3/2o   . |   3 |    3 |    * 2400 |   1   1
--------------+-----+------+-----------+--------
o3/2x3/2o   . ♦   6 |   12 |    4    4 | 600   *
.   x3/2o5/4o ♦  12 |   30 |    0   20 |   * 120

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