Acronym cont
Name tetracontoctachoron,
octagonny,
bitruncated icositetrachoron
 
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Cross sections
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Circumradius 2+sqrt(2) = 3.414214
Vertex figure
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Vertex layers
LayerSymmetrySubsymmetries
 o3o4o3o o3o4o . o3o . o o . o3o . o4o3o
1o3x4x3o o3x4x .
tic first
o3x . o
{3} first
o . x3o
{3} first
. x4x3o
tic first
2 o3w4o . o3w . x x . w3o . o4w3o
3 x3w4o . x3w . w w . w3x . o4w3x
4 w3x4x . w3x . X X . x3w . x4x3w
5 w3o4w . w3w . w w . w3w . w4o3w
6 x3o4X . w3o . W W . o3w . X4o3x
7a w3o4w . X3w . x x . w3X . w4o3w
7b x3o . Y Y . o3x
8 w3x4x . W3x . o o . x3W . x4x3w
9 x3w4o . w3X . w w . X3w . o4w3x
10 o3w4o . w3o . Y Y . o3w . o4w3o
11 o3x4x .
opposite tic
x3W . w w . W3x . x4x3o
opposite tic
12   Y3o . o o . o3Y  
13 w3X . X X . X3w
14a o3Y . x x . Y3o
14b w3x . Y Y . x3w
15 w3w . W W . w3w
16a Y3o . x x . o3Y
16b x3w . Y Y . w3x
17 X3w . X X . w3X
18 o3Y . o o . Y3o
19 W3x . w w . x3W
20 o3w . Y Y . w3o
21 X3w . w w . w3X
22 x3W . o o . W3x
23a w3X . x x . X3w
23b o3x . Y Y . x3o
24 o3w . W W . w3o
25 w3w . w w . w3w
26 x3w . X X . w3x
27 w3x . w w . x3w
28 w3o . x x . o3w
29 x3o . o
opposite {3}
o . o3x
opposite {3}
(X=x+w=2x+q, W=2x+2q, Y=3x+2q)
Lace city
in approx. ASCII-art
 ©  
              x4x   w4o     w4o   x4x              
                                                   
          o4w           X4o           o4w          
                                                   
                                                   
    o4w   o4X           X4x           o4X   o4w    
                                                   
x4x           x4X   w4w     w4w   x4X           x4x
                                                   
                                                   
w4o           w4w                 w4w           w4o
                                                   
    X4o   X4x                         X4x   X4o    		X=x+w=2x+q
                                                   
w4o           w4w                 w4w           w4o
                                                   
                                                   
x4x           x4X   w4w     w4w   x4X           x4x
                                                   
    o4w   o4X           X4x           o4X   o4w    
                                                   
                                                   
          o4w           X4o           o4w          
                                                   
              x4x   w4o     w4o   x4x              
 ©  
            x3o w3o   w3x x3w   o3w o3x            
                                                   
          w3o           w3w           o3w          
                                                   
                                                   
       w3x           w3X   X3w           x3w       
                                                   
     x3w w3w   w3X x3W       W3x X3w   w3w w3x     
                                                   
                                                   
  o3w       X3w       o3Y Y3o       w3X       w3o  		X=wq=x+w=2x+q, W=2w=2x+2q, Y=ww=3x+2q
                                                   
o3x           W3x   Y3o     o3Y   x3W           x3o
                                                   
  o3w       X3w       o3Y Y3o       w3X       w3o  
                                                   
                                                   
     x3w w3w   w3X x3W       W3x X3w   w3w w3x     
                                                   
       w3x           w3X   X3w           x3w       
                                                   
                                                   
          w3o           w3w           o3w          
                                                   
            x3o w3o   w3x x3w   o3w o3x            
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: tic
cont 48
)
Dihedral angles
  • at {8} between tic and tic:   135°
  • at {3} between tic and tic:   120°
Dual o3m4m3o
Confer
Grünbaumian relatives:
2cont  
decompositions:
srico || cont  
general polytopal classes:
noble polytopes   partial Stott expansions  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

As abstract polytope cont is isomorphic to gic, thereby replacing the octagons by octagrams, resp. replacing tic by quith.

Note that cont can be thought of as the external blend of 1 srico + 24 sircoatics + 96 triddips + 24 coatics. This decomposition is described as the degenerate segmentoteron xo3ox4xx3oo&#x.


Incidence matrix according to Dynkin symbol

o3x4x3o

. . . . | 288 |   2   2 |  1   4  1 |  2  2
--------+-----+---------+-----------+------
. x . . |   2 | 288   * |  1   2  0 |  2  1
. . x . |   2 |   * 288 |  0   2  1 |  1  2
--------+-----+---------+-----------+------
o3x . . |   3 |   3   0 | 96   *  * |  2  0
. x4x . |   8 |   4   4 |  * 144  * |  1  1
. . x3o |   3 |   0   3 |  *   * 96 |  0  2
--------+-----+---------+-----------+------
o3x4x .   24 |  24  12 |  8   6  0 | 24  *
. x4x3o   24 |  12  24 |  0   6  8 |  * 24
or
. . . .    | 288 |   4 |   2   4 |  4
-----------+-----+-----+---------+---
. x . .  & |   2 | 576 |   1   2 |  3
-----------+-----+-----+---------+---
o3x . .  & |   3 |   3 | 192   * |  2
. x4x .    |   8 |   8 |   * 144 |  2
-----------+-----+-----+---------+---
o3x4x .  &   24 |  36 |   8   6 | 48

snubbed forms: o3β4x3o, o3β4β3o

o3x4x3/2o

. . .   . | 288 |   2   2 |  1   4  1 |  2  2
----------+-----+---------+-----------+------
. x .   . |   2 | 288   * |  1   2  0 |  2  1
. . x   . |   2 |   * 288 |  0   2  1 |  1  2
----------+-----+---------+-----------+------
o3x .   . |   3 |   3   0 | 96   *  * |  2  0
. x4x   . |   8 |   4   4 |  * 144  * |  1  1
. . x3/2o |   3 |   0   3 |  *   * 96 |  0  2
----------+-----+---------+-----------+------
o3x4x   .   24 |  24  12 |  8   6  0 | 24  *
. x4x3/2o   24 |  12  24 |  0   6  8 |  * 24

o3/2x4x3/2o

.   . .   . | 288 |   2   2 |  1   4  1 |  2  2
------------+-----+---------+-----------+------
.   x .   . |   2 | 288   * |  1   2  0 |  2  1
.   . x   . |   2 |   * 288 |  0   2  1 |  1  2
------------+-----+---------+-----------+------
o3/2x .   . |   3 |   3   0 | 96   *  * |  2  0
.   x4x   . |   8 |   4   4 |  * 144  * |  1  1
.   . x3/2o |   3 |   0   3 |  *   * 96 |  0  2
------------+-----+---------+-----------+------
o3/2x4x   .   24 |  24  12 |  8   6  0 | 24  *
.   x4x3/2o   24 |  12  24 |  0   6  8 |  * 24
or
.   . .   .    | 288 |   4 |   2   4 |  4
---------------+-----+-----+---------+---
.   x .   .  & |   2 | 576 |   1   2 |  3
---------------+-----+-----+---------+---
o3/2x .   .  & |   3 |   3 | 192   * |  2
.   x4x   .    |   8 |   8 |   * 144 |  2
---------------+-----+-----+---------+---
o3/2x4x   .  &   24 |  36 |   8   6 | 48

wx3oo3xw4xo&#zx   → height = 0
(tegum sum of (w,x,x)-proh and (x,w)-rico)

o.3o.3o.4o.     | 192  * |   2  1   1  0 |  1  2  2  1  0 | 1  1  2
.o3.o3.o4.o     |   * 96 |   0  0   2  2 |  0  0  4  1  1 | 0  2  2
----------------+--------+---------------+----------------+--------
.. .. x. ..     |   2  0 | 192  *   *  * |  1  1  1  0  0 | 1  1  1
.. .. .. x.     |   2  0 |   * 96   *  * |  0  2  0  1  0 | 1  0  2
oo3oo3oo4oo&#x  |   1  1 |   *  * 192  * |  0  0  2  1  0 | 0  1  2
.x .. .. ..     |   0  2 |   *  *   * 96 |  0  0  2  0  1 | 0  2  1
----------------+--------+---------------+----------------+--------
.. o.3x. ..     |   3  0 |   3  0   0  0 | 64  *  *  *  * | 1  1  0
.. .. x.4x.     |   8  0 |   4  4   0  0 |  * 48  *  *  * | 1  0  1
wx .. xw ..&#zx |   4  4 |   2  0   4  2 |  *  * 96  *  * | 0  1  1
.. .. .. xo&#x  |   2  1 |   0  1   2  0 |  *  *  * 96  * | 0  0  2
.x3.o .. ..     |   0  3 |   0  0   0  3 |  *  *  *  * 32 | 0  2  0
----------------+--------+---------------+----------------+--------
.. o.3x.4x.       24  0 |  24 12   0  0 |  8  6  0  0  0 | 8  *  *
wx3oo3xw ..&#zx   12 12 |  12  0  12 12 |  4  0  6  0  4 | * 16  *
wx .. xw4xo&#zx   16  8 |   8  8  16  4 |  0  2  4  8  0 | *  * 24

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