tetacoaoct

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°
Face vector	22, 78, 86, 30
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 though, 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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