Acronym	octaco, K-4.29
Name	octahedron atop cuboctahedron, half of icositetrachoron (its oct-first rotunda), rectified octahedron-pyramid
Segmentochoron display
Circumradius	1
Vertex figure	cube, xx oq&#x
Lace city in approx. ASCII-art	o3x x3o x3o x3x o3x
	o4o x4o o4o x4o o4q x4o
Volume	1
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	at {3} between oct and oct:   120° at {3} between oct and squippy:   120° at {4} between squippy and co:   90° at {3} between oct and co:   60°
Face vector	18, 60, 58, 16
Confer	uniform relative: ico   related segmentochora: oct || tricu   {6} || oct   {4} || co   squippy || co   hoctaoho   octacho   hothahacho   related CRFs: oct || co || co || oct   oct || co || tet   ambification pre-image: octpy   general polytopal classes: segmentochora   fundamental lace prisms   lace simplices
External links

Incidence matrix according to Dynkin symbol

xo3ox4oo&#x   → height = 1/sqrt(2) = 0.707107
(oct || co)

o.3o.4o.    | 6  * ♦  4  4  0 | 4  4  4 0 0 | 1 4 1 0
.o3.o4.o    | * 12 |  0  2  4 | 0  1  4 2 2 | 0 2 2 1
------------+------+----------+-------------+--------
x. .. ..    | 2  0 | 12  *  * | 2  1  0 0 0 | 1 2 0 0
oo3oo4oo&#x | 1  1 |  * 24  * | 0  1  2 0 0 | 0 2 1 0
.. .x ..    | 0  2 |  *  * 24 | 0  0  1 1 1 | 0 1 1 1
------------+------+----------+-------------+--------
x.3o. ..    | 3  0 |  3  0  0 | 8  *  * * * | 1 1 0 0
xo .. ..&#x | 2  1 |  1  2  0 | * 12  * * * | 0 2 0 0
.. ox ..&#x | 1  2 |  0  2  1 | *  * 24 * * | 0 1 1 0
.o3.x ..    | 0  3 |  0  0  3 | *  *  * 8 * | 0 1 0 1
.. .x4.o    | 0  4 |  0  0  4 | *  *  * * 6 | 0 0 1 1
------------+------+----------+-------------+--------
x.3o.4o.    ♦ 6  0 | 12  0  0 | 8  0  0 0 0 | 1 * * *
xo3ox ..&#x ♦ 3  3 |  3  6  3 | 1  3  3 1 0 | * 8 * *
.. ox4oo&#x ♦ 1  4 |  0  4  4 | 0  0  4 0 1 | * * 6 *
.o3.x4.o    ♦ 0 12 |  0  0 24 | 0  0  0 8 6 | * * * 1

ox3xo3ox&#x   → height = 1/sqrt(2) = 0.707107
(oct || co)

o.3o.3o.    | 6  * ♦  4  4  0  0 | 2 2  2  4  2 0 0 0 | 1 2 1 2 0
.o3.o3.o    | * 12 |  0  2  2  2 | 0 0  2  1  2 1 2 1 | 0 1 2 1 1
------------+------+-------------+--------------------+----------
.. x. ..    | 2  0 | 12  *  *  * | 1 1  0  1  0 0 0 0 | 1 1 0 1 0
oo3oo3oo&#x | 1  1 |  * 24  *  * | 0 0  1  1  1 0 0 0 | 0 1 1 1 0
.x .. ..    | 0  2 |  *  * 12  * | 0 0  1  0  0 1 1 0 | 0 1 1 0 1
.. .. .x    | 0  2 |  *  *  * 12 | 0 0  0  0  1 0 1 1 | 0 0 1 1 1
------------+------+-------------+--------------------+----------
o.3x. ..    | 3  0 |  3  0  0  0 | 4 *  *  *  * * * * | 1 1 0 0 0
.. x.3o.    | 3  0 |  3  0  0  0 | * 4  *  *  * * * * | 1 0 0 1 0
ox .. ..&#x | 1  2 |  0  2  1  0 | * * 12  *  * * * * | 0 1 1 0 0
.. xo ..&#x | 2  1 |  1  2  0  0 | * *  * 12  * * * * | 0 1 0 1 0
.. .. ox&#x | 1  2 |  0  2  0  1 | * *  *  * 12 * * * | 0 0 1 1 0
.x3.o ..    | 0  3 |  0  0  3  0 | * *  *  *  * 4 * * | 0 1 0 0 1
.x .. .x    | 0  4 |  0  0  2  2 | * *  *  *  * * 6 * | 0 0 1 0 1
.. .o3.x    | 0  3 |  0  0  0  3 | * *  *  *  * * * 4 | 0 0 0 1 1
------------+------+-------------+--------------------+----------
o.3x.3o.    ♦ 6  0 | 12  0  0  0 | 4 4  0  0  0 0 0 0 | 1 * * * *
ox3xo ..&#x ♦ 3  3 |  3  6  3  0 | 1 0  3  3  0 1 0 0 | * 4 * * *
ox .. ox&#x ♦ 1  4 |  0  4  2  2 | 0 0  2  0  2 0 1 0 | * * 6 * *
.. xo3ox&#x ♦ 3  3 |  3  6  0  3 | 0 1  0  3  3 0 0 1 | * * * 4 *
.x3.o3.x    ♦ 0 12 |  0  0 12 12 | 0 0  0  0  0 4 6 4 | * * * * 1

{3} || pseudo tricu || oct   → both heights = 1/sqrt(2) = 0.707107

3 * * * * | 2 2 2 0 0 0 0 0 0 0 0 0 0 | 1 2 2 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0 0 0 A
* 6 * * * | 0 1 0 1 1 1 1 1 0 0 0 0 0 | 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 | 1 0 1 1 1 1 0 0 B
* * 3 * * ♦ 0 0 2 0 0 2 0 0 2 2 0 0 0 | 0 0 1 0 2 2 1 0 0 0 2 0 1 1 2 0 0 0 0 | 0 1 1 2 1 0 1 0 C
* * * 3 * | 0 0 0 0 0 0 2 0 0 0 2 2 0 | 0 0 0 0 0 0 0 1 2 0 0 2 0 0 0 1 1 2 0 | 1 0 0 0 1 2 0 1 D
* * * * 3 ♦ 0 0 0 0 0 0 0 2 0 2 0 2 2 | 0 0 0 0 0 0 0 0 0 1 2 2 0 2 1 0 2 1 1 | 0 0 0 1 2 1 1 1 E
----------+---------------------------+---------------------------------------+----------------
2 0 0 0 0 | 3 * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0
1 1 0 0 0 | * 6 * * * * * * * * * * * | 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 0 0
1 0 1 0 0 | * * 6 * * * * * * * * * * | 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0
0 2 0 0 0 | * * * 3 * * * * * * * * * | 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 | 1 0 1 0 1 0 0 0
0 2 0 0 0 | * * * * 3 * * * * * * * * | 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 | 1 0 0 1 0 1 0 0
0 1 1 0 0 | * * * * * 6 * * * * * * * | 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 | 0 0 1 1 1 0 0 0
0 1 0 1 0 | * * * * * * 6 * * * * * * | 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 | 1 0 0 0 1 1 0 0
0 1 0 0 1 | * * * * * * * 6 * * * * * | 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 | 0 0 0 1 1 1 0 0
0 0 2 0 0 | * * * * * * * * 3 * * * * | 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 | 0 1 0 1 0 0 1 0
0 0 1 0 1 | * * * * * * * * * 6 * * * | 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 | 0 0 0 1 1 0 1 0
0 0 0 2 0 | * * * * * * * * * * 3 * * | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 | 1 0 0 0 0 1 0 1
0 0 0 1 1 | * * * * * * * * * * * 6 * | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 | 0 0 0 0 1 1 0 1
0 0 0 0 2 | * * * * * * * * * * * * 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 | 0 0 0 0 1 0 1 1
----------+---------------------------+---------------------------------------+----------------
3 0 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0
2 2 0 0 0 | 1 2 0 1 0 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0
2 0 1 0 0 | 1 0 2 0 0 0 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0
1 2 0 0 0 | 0 2 0 0 1 0 0 0 0 0 0 0 0 | * * * 3 * * * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0
1 1 1 0 0 | 0 1 1 0 0 1 0 0 0 0 0 0 0 | * * * * 6 * * * * * * * * * * * * * * | 0 0 1 1 0 0 0 0
1 0 2 0 0 | 0 0 2 0 0 0 0 0 1 0 0 0 0 | * * * * * 3 * * * * * * * * * * * * * | 0 1 0 1 0 0 0 0
0 2 1 0 0 | 0 0 0 1 0 2 0 0 0 0 0 0 0 | * * * * * * 3 * * * * * * * * * * * * | 0 0 1 0 1 0 0 0
0 2 0 1 0 | 0 0 0 1 0 0 2 0 0 0 0 0 0 | * * * * * * * 3 * * * * * * * * * * * | 1 0 0 0 1 0 0 0
0 2 0 2 0 | 0 0 0 0 1 0 2 0 0 0 1 0 0 | * * * * * * * * 3 * * * * * * * * * * | 1 0 0 0 0 1 0 0
0 2 0 0 1 | 0 0 0 0 1 0 0 2 0 0 0 0 0 | * * * * * * * * * 3 * * * * * * * * * | 0 0 0 1 0 1 0 0
0 1 1 0 1 | 0 0 0 0 0 1 0 1 0 1 0 0 0 | * * * * * * * * * * 6 * * * * * * * * | 0 0 0 1 1 0 0 0
0 1 0 1 1 | 0 0 0 0 0 0 1 1 0 0 0 1 0 | * * * * * * * * * * * 6 * * * * * * * | 0 0 0 0 1 1 0 0
0 0 3 0 0 | 0 0 0 0 0 0 0 0 3 0 0 0 0 | * * * * * * * * * * * * 1 * * * * * * | 0 1 0 0 0 0 1 0
0 0 1 0 2 | 0 0 0 0 0 0 0 0 0 2 0 0 1 | * * * * * * * * * * * * * 3 * * * * * | 0 0 0 0 1 0 1 0
0 0 2 0 1 | 0 0 0 0 0 0 0 0 1 2 0 0 0 | * * * * * * * * * * * * * * 3 * * * * | 0 0 0 1 0 0 1 0
0 0 0 3 0 | 0 0 0 0 0 0 0 0 0 0 3 0 0 | * * * * * * * * * * * * * * * 1 * * * | 1 0 0 0 0 0 0 1
0 0 0 1 2 | 0 0 0 0 0 0 0 0 0 0 0 2 1 | * * * * * * * * * * * * * * * * 3 * * | 0 0 0 0 1 0 0 1
0 0 0 2 1 | 0 0 0 0 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * * * * * * * 3 * | 0 0 0 0 0 1 0 1
0 0 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 1 1
----------+---------------------------+---------------------------------------+----------------
3 6 0 3 0 | 3 6 0 3 3 0 6 0 0 0 3 0 0 | 1 3 0 3 0 0 0 3 3 0 0 0 0 0 0 1 0 0 0 | 1 * * * * * * * co
3 0 3 0 0 | 3 0 6 0 0 0 0 0 3 0 0 0 0 | 1 0 3 0 0 3 0 0 0 0 0 0 1 0 0 0 0 0 0 | * 1 * * * * * * oct
2 2 1 0 0 | 1 2 2 1 0 2 0 0 0 0 0 0 0 | 0 1 1 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | * * 3 * * * * * squippy
1 2 2 0 1 | 0 2 2 0 1 2 0 2 1 2 0 0 0 | 0 0 0 1 2 1 0 0 0 1 2 0 0 0 1 0 0 0 0 | * * * 3 * * * * oct
0 2 1 1 2 | 0 0 0 1 0 2 2 2 0 2 0 2 1 | 0 0 0 0 0 0 1 1 0 0 2 2 0 1 0 0 1 0 0 | * * * * 3 * * * oct
0 2 0 2 1 | 0 0 0 0 1 0 2 2 0 0 1 2 0 | 0 0 0 0 0 0 0 0 1 1 0 2 0 0 0 0 0 1 0 | * * * * * 3 * * squippy
0 0 3 0 3 | 0 0 0 0 0 0 0 0 3 6 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 0 0 0 1 | * * * * * * 1 * oct
0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 0 3 6 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1 | * * * * * * * 1 oct

      x3o   
      A     
   x3x   o3x
   B     C  
o3x   x3o   
D     E