Acronym reco
Name rectified cuboctahedron,
variation of small rhombicuboctahedron,
Waterman polyhedron number 6 wrt. primitive cubic lattice C3 centered at a lattice point,
Waterman polyhedron number 3 wrt. face-centered cubic lattice A3 centered at a lattice point
 
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Circumradius sqrt(3) = 1.732051
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between x3o and x . q:   arccos[-sqrt(2/3)] = 144.735610°
  • between x . q and o4q:   135°
Face vector 24, 48, 26
Confer
uniform variant:
sirco  
variations:
a3b4c   q3o4x   f3o4x   u3o4x  
ambification pre-image:
co  
general polytopal classes:
ambifications  

Measures are using edge sizes x = 1 and q = sqrt(2) = 1.414214.

Rectification wrt. a non-regular polytope is meant to be the singular instance of truncations on all vertices at such a depth that the hyperplane intersections on the former edges will coincide (provided such a choice exists). Within the specific case of co all edges belong to a single orbit of symmetry, i.e. rectification clearly is applicable, without any recourse to Conway's ambification (chosing the former edge centers generally).


Incidence matrix according to Dynkin symbol

x3o4q

. . . | 24 |  2  2 | 1  2 1
------+----+-------+-------
x . . |  2 | 24  * | 1  1 0
. . q |  2 |  * 24 | 0  1 1
------+----+-------+-------
x3o . |  3 |  3  0 | 8  * *
x . q |  4 |  2  2 | * 12 *
. o4q |  4 |  0  4 | *  * 6

q4/3o3/2x

.   .   . | 24 |  2  2 | 1  2 1
----------+----+-------+-------
q   .   . |  2 | 24  * | 1  1 0
.   .   x |  2 |  * 24 | 0  1 1
----------+----+-------+-------
q4/3o   . |  4 |  4  0 | 6  * *
q   .   x |  4 |  2  2 | * 12 *
.   o3/2x |  3 |  0  3 | *  * 8

uo3xx3ou&#zq   → height = 0

o.3o.3o.     | 12  * |  2  2  0 | 1 1  2 0
.o3.o3.o     |  * 12 |  0  2  2 | 0 1  2 1
-------------+-------+----------+---------
.. x. ..     |  2  0 | 12  *  * | 1 0  1 0
oo3oo3oo&#q  |  1  1 |  * 24  * | 0 1  1 0
.. .x ..     |  0  2 |  *  * 12 | 0 0  1 1
-------------+-------+----------+---------
.. x.3o.     |  3  0 |  3  0  0 | 4 *  * *
uo .. ou&#zq |  2  2 |  0  4  0 | * 6  * *
.. xx ..&#q  |  2  2 |  1  2  1 | * * 12 *
.o3.x ..     |  0  3 |  0  0  3 | * *  * 4
or
o.3o.3o.     & | 24 |  2  2 | 1 1  2
---------------+----+-------+-------
.. x. ..     & |  2 | 24  * | 1 0  1
oo3oo3oo&#q    |  2 |  * 24 | 0 1  1
---------------+----+-------+-------
.. x.3o.     & |  3 |  3  0 | 8 *  *
uo .. ou&#zq   |  4 |  0  4 | * 6  *
.. xx ..&#q    |  4 |  2  2 | * * 12

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