Acronym tetacoaoct
Name octahedron atop (pseudo) cuboctahedron atop tetrahedron
Circumradius 1
Lace city
in approx. ASCII-art
   o3x   x3o   		-- o3x3o (oct)
               
x3o   x3x   o3x		-- x3o3x (co)
               
               
    x3o   o3o  		-- x3o3o (tet)
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {4} between squippy and trip:   arccos[-sqrt(5/6)] = 155.905157°
  • at {3} between oct and tet:   arccos(-[3 sqrt(5)-1]/8) = 135.522488°
  • at {4} between trip and trip:   arccos(-2/3) = 131.810315°
  • at {3} between tet and trip:   arccos(-sqrt(3/8)) = 127.761244°
  • at {3} between oct and oct:   120°
  • at {3} between oct and squippy:   120°
  • at {3} between oct and trip:   arccos(-sqrt[9-3 sqrt(5)]/4) = 112.238756°
Confer
uniform relative:
ico   spid  
related segmentochora:
octaco   tetaco  
general polytopal classes:
bistratic lace towers  

This polychoron is quite simply obtained as an external blend of the rotundae of ico and spid respectively, thereby blending out the joined co bases each. Even so, this mere stack of segmentochora happens to be both convex and circumscribable.


Incidence matrix according to Dynkin symbol

oxx3xoo3oxo&#x   → height(1,2) = 1/sqrt(2) = 0.707107
                   height(2,3) = sqrt(5/8) = 0.790569
(oct || pseudo co || tet)

o..3o..3o..    | 6  * *   4  4  0  0  0 0 | 2 2  2  4  2 0 0 0  0  0 0 | 1 2 1 2 0 0 0 0
.o.3.o.3.o.    | * 12 * |  0  2  2  2  1 0 | 0 0  2  1  2 1 2 1  2  2 0 | 0 1 2 1 1 2 1 0
..o3..o3..o    | *  * 4   0  0  0  0  3 3 | 0 0  0  0  0 0 0 0  6  3 3 | 0 0 0 0 3 3 1 1
---------------+--------+------------------+----------------------------+----------------
... x.. ...    | 2  0 0 | 12  *  *  *  * * | 1 1  0  1  0 0 0 0  0  0 0 | 1 1 0 1 0 0 0 0
oo.3oo.3oo.&#x | 1  1 0 |  * 24  *  *  * * | 0 0  1  1  1 0 0 0  0  0 0 | 0 1 1 1 0 0 0 0
.x. ... ...    | 0  2 0 |  *  * 12  *  * * | 0 0  1  0  0 1 1 0  1  0 0 | 0 1 1 0 1 1 0 0
... ... .x.    | 0  2 0 |  *  *  * 12  * * | 0 0  0  0  1 0 1 1  0  1 0 | 0 0 1 1 0 1 1 0
.oo3.oo3.oo&#x | 0  1 1 |  *  *  *  * 12 * | 0 0  0  0  0 0 0 0  2  2 0 | 0 0 0 0 1 2 1 0
..x ... ...    | 0  0 2 |  *  *  *  *  * 6 | 0 0  0  0  0 0 0 0  2  0 2 | 0 0 0 0 2 1 0 1
---------------+--------+------------------+----------------------------+----------------
o..3x.. ...    | 3  0 0 |  3  0  0  0  0 0 | 4 *  *  *  * * * *  *  * * | 1 1 0 0 0 0 0 0
... x..3o..    | 3  0 0 |  3  0  0  0  0 0 | * 4  *  *  * * * *  *  * * | 1 0 0 1 0 0 0 0
ox. ... ...&#x | 1  2 0 |  0  2  1  0  0 0 | * * 12  *  * * * *  *  * * | 0 1 1 0 0 0 0 0
... xo. ...&#x | 2  1 0 |  1  2  0  0  0 0 | * *  * 12  * * * *  *  * * | 0 1 0 1 0 0 0 0
... ... ox.&#x | 1  2 0 |  0  2  0  1  0 0 | * *  *  * 12 * * *  *  * * | 0 0 1 1 0 0 0 0
.x.3.o. ...    | 0  3 0 |  0  0  3  0  0 0 | * *  *  *  * 4 * *  *  * * | 0 1 0 0 1 0 0 0
.x. ... .x.    | 0  4 0 |  0  0  2  2  0 0 | * *  *  *  * * 6 *  *  * * | 0 0 1 0 0 1 0 0
... .o.3.x.    | 0  3 0 |  0  0  0  3  0 0 | * *  *  *  * * * 4  *  * * | 0 0 0 1 0 0 1 0
.xx ... ...&#x | 0  2 2 |  0  0  1  0  2 1 | * *  *  *  * * * * 12  * * | 0 0 0 0 1 1 0 0
... ... .xo&#x | 0  2 1 |  0  0  0  1  2 0 | * *  *  *  * * * *  * 12 * | 0 0 0 0 0 1 1 0
..x3..o ...    | 0  0 3 |  0  0  0  0  0 3 | * *  *  *  * * * *  *  * 4 | 0 0 0 0 1 0 0 1
---------------+--------+------------------+----------------------------+----------------
o..3x..3o..     6  0 0 | 12  0  0  0  0 0 | 4 4  0  0  0 0 0 0  0  0 0 | 1 * * * * * * *
ox.3xo. ...&#x  3  3 0 |  3  6  3  0  0 0 | 1 0  3  3  0 1 0 0  0  0 0 | * 4 * * * * * *
ox. ... ox.&#x  1  4 0 |  0  4  2  2  0 0 | 0 0  2  0  2 0 1 0  0  0 0 | * * 6 * * * * *
... xo.3ox.&#x  3  3 0 |  3  6  0  3  0 0 | 0 1  0  3  3 0 0 1  0  0 0 | * * * 4 * * * *
.xx3.oo ...&#x  0  3 3 |  0  0  3  0  3 3 | 0 0  0  0  0 1 0 0  3  0 1 | * * * * 4 * * *
.xx ... .xo&#x  0  4 2 |  0  0  2  2  4 1 | 0 0  0  0  0 0 1 0  2  2 0 | * * * * * 6 * *
... .oo3.xo&#x  0  3 1 |  0  0  0  3  3 0 | 0 0  0  0  0 0 0 1  0  3 0 | * * * * * * 4 *
..x3..o3..o     0  0 4 |  0  0  0  0  0 6 | 0 0  0  0  0 0 0 0  0  0 4 | * * * * * * * 1

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