Acronym	octatricu, oct || tricu, K-4.30
Name	octahedron atop trigonal cupola, 2/6-luna of icositetrachoron
Segmentochoron display
Circumradius	1
Lace city in approx. ASCII-art	o3x x3o x3o x3x
Coordinates	(1, 0, 0; 1)/sqrt(2)           & permutations in all but last coord, all changes of sign in all but last coord (oct layer) (1, -1, 0; 0)/sqrt(2)           & permutations in all but last coord ({6}-base of tricu layer) (1, 1, 0; 0)/sqrt(2)           & permutations in all but last coord ({3}-base of tricu layer)
Volume	2/3 = 0.666667
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 {3} between squippy and squippy:   120° at {6} between tricu and tricu:   120° at {4} between squippy and tricu:   90° at {3} between oct and tricu:   60°
Face vector	15, 45, 43, 13
Confer	related CRFs: oct || co   squippy || tricu   {6} || oct   uniform relative: ico   general polytopal classes: luna   segmentochora
External links

Incidence matrix according to Dynkin symbol

xoxx3oxox&#xr   → all heights = sqrt(2/3) = 0.816497

o...3o...     | 3 * * * | 2 2 2 0 0 0 0 0 0 0 | 1 2 1 2 1 2 0 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0 0
.o..3.o..     | * 3 * * ♦ 0 2 0 2 2 2 0 0 0 0 | 0 1 2 0 0 2 1 1 2 1 2 0 0 0 0 | 1 0 1 2 1 1 0
..o.3..o.     | * * 3 * | 0 0 0 0 2 0 2 2 0 0 | 0 0 0 0 0 0 0 2 1 0 2 1 2 1 0 | 0 0 0 1 1 2 1
...o3...3     | * * * 6 | 0 0 1 0 0 1 0 1 1 1 | 0 0 0 1 1 1 0 0 0 1 1 0 1 1 1 | 0 1 1 1 0 1 1
--------------+---------+---------------------+-------------------------------+--------------
x... ....     | 2 0 0 0 | 3 * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0
oo..3oo..&#x  | 1 1 0 0 | * 6 * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 0
o..o3o..o&#x  | 1 0 0 1 | * * 6 * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0
.... .x..     | 0 2 0 0 | * * * 3 * * * * * * | 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 | 1 0 0 1 1 0 0
.oo.3.oo.&#x  | 0 1 1 0 | * * * * 6 * * * * * | 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 | 0 0 0 1 1 1 0
.o.o3.o.o&#x  | 0 1 0 1 | * * * * * 6 * * * * | 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 | 0 0 1 1 0 1 0
..x. ....     | 0 0 2 0 | * * * * * * 3 * * * | 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 | 0 0 0 0 1 1 1
..oo3..oo&#x  | 0 0 1 1 | * * * * * * * 6 * * | 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 | 0 0 0 1 0 1 1
...x ....     | 0 0 0 2 | * * * * * * * * 3 * | 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 | 0 1 1 0 0 1 1
.... ...x     | 0 0 0 2 | * * * * * * * * * 3 | 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 | 0 1 0 1 0 0 1
--------------+---------+---------------------+-------------------------------+--------------
x...3o...     | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * | 1 1 0 0 0 0 0
xo.. ....&#x  | 2 1 0 0 | 1 2 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * | 1 0 1 0 0 0 0
.... ox..&#x  | 1 2 0 0 | 0 2 0 1 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * | 1 0 0 1 0 0 0
x..x ....&#x  | 2 0 0 2 | 1 0 2 0 0 0 0 0 1 0 | * * * 3 * * * * * * * * * * * | 0 1 1 0 0 0 0
.... o..x&#x  | 1 0 0 2 | 0 0 2 0 0 0 0 0 0 1 | * * * * 3 * * * * * * * * * * | 0 1 0 1 0 0 0
oo.o3oo.o&#x  | 1 1 0 1 | 0 1 1 0 0 1 0 0 0 0 | * * * * * 6 * * * * * * * * * | 0 0 1 1 0 0 0
.o..3.x..     | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 0 | * * * * * * 1 * * * * * * * * | 1 0 0 0 1 0 0
.ox. ....&#x  | 0 1 2 0 | 0 0 0 0 2 0 1 0 0 0 | * * * * * * * 3 * * * * * * * | 0 0 0 0 1 1 0
.... .xo.&#x  | 0 2 1 0 | 0 0 0 1 2 0 0 0 0 0 | * * * * * * * * 3 * * * * * * | 0 0 0 1 1 0 0
.o.x ....&#x  | 0 1 0 2 | 0 0 0 0 0 2 0 0 1 0 | * * * * * * * * * 3 * * * * * | 0 0 1 0 0 1 0
.ooo3.ooo&#x  | 0 1 1 1 | 0 0 0 0 1 1 0 1 0 0 | * * * * * * * * * * 6 * * * * | 0 0 0 1 0 1 0
..x.3..o.     | 0 0 3 0 | 0 0 0 0 0 0 3 0 0 0 | * * * * * * * * * * * 1 * * * | 0 0 0 0 1 0 1
..xx ....&#x  | 0 0 2 2 | 0 0 0 0 0 0 1 2 1 0 | * * * * * * * * * * * * 3 * * | 0 0 0 0 0 1 1
.... ..ox&#x  | 0 0 1 2 | 0 0 0 0 0 0 0 2 0 1 | * * * * * * * * * * * * * 3 * | 0 0 0 1 0 0 1
...x3...x     | 0 0 0 6 | 0 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * * * * 1 | 0 1 0 0 0 0 1
--------------+---------+---------------------+-------------------------------+--------------
xo..3ox..&#x  ♦ 3 3 0 0 | 3 6 0 3 0 0 0 0 0 0 | 1 3 3 0 0 0 1 0 0 0 0 0 0 0 0 | 1 * * * * * *
x..x3o..x&#x  ♦ 3 0 0 6 | 3 0 6 0 0 0 0 0 3 3 | 1 0 0 3 3 0 0 0 0 0 0 0 0 0 1 | * 1 * * * * *
xo.x ....&#x  ♦ 2 1 0 2 | 1 2 2 0 0 2 0 0 1 0 | 0 1 0 1 0 2 0 0 0 1 0 0 0 0 0 | * * 3 * * * *
.... oxox&#xr ♦ 1 2 1 2 | 0 2 2 1 2 2 0 2 0 1 | 0 0 1 0 1 2 0 0 1 0 2 0 0 1 0 | * * * 3 * * *
.ox.3.xo.&#x  ♦ 0 3 3 0 | 0 0 0 3 6 0 3 0 0 0 | 0 0 0 0 0 0 1 3 3 0 0 1 0 0 0 | * * * * 1 * *
.oxx ....&#x  ♦ 0 1 2 2 | 0 0 0 0 2 2 1 2 1 0 | 0 0 0 0 0 0 0 1 0 1 2 0 1 0 0 | * * * * * 3 *
..xx3..ox&#x  ♦ 0 0 3 6 | 0 0 0 0 0 0 3 6 3 3 | 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1 | * * * * * * 1

oct || tricu   → height = 1/sqrt(2) = 0.707107

o...3o...     | 3 * * * | 2 2 2 0 0 0 0 0 0 0 | 1 2 1 2 1 2 0 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0 0
.o..3.o..     | * 3 * * ♦ 0 2 0 2 2 2 0 0 0 0 | 0 1 2 0 0 2 1 1 2 1 2 0 0 0 0 | 1 0 1 2 1 1 0
..o.3..o.     | * * 3 * | 0 0 0 0 2 0 2 2 0 0 | 0 0 0 0 0 0 0 2 1 0 2 1 2 1 0 | 0 0 0 1 1 2 1
...o3...3     | * * * 6 | 0 0 1 0 0 1 0 1 1 1 | 0 0 0 1 1 1 0 0 0 1 1 0 1 1 1 | 0 1 1 1 0 1 1
--------------+---------+---------------------+-------------------------------+--------------
x... ....     | 2 0 0 0 | 3 * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0
oo..3oo..&#x  | 1 1 0 0 | * 6 * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 0
o..o3o..o&#x  | 1 0 0 1 | * * 6 * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0
.... .x..     | 0 2 0 0 | * * * 3 * * * * * * | 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 | 1 0 0 1 1 0 0
.oo.3.oo.&#x  | 0 1 1 0 | * * * * 6 * * * * * | 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 | 0 0 0 1 1 1 0
.o.o3.o.o&#x  | 0 1 0 1 | * * * * * 6 * * * * | 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 | 0 0 1 1 0 1 0
..x. ....     | 0 0 2 0 | * * * * * * 3 * * * | 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 | 0 0 0 0 1 1 1
..oo3..oo&#x  | 0 0 1 1 | * * * * * * * 6 * * | 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 | 0 0 0 1 0 1 1
...x ....     | 0 0 0 2 | * * * * * * * * 3 * | 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 | 0 1 1 0 0 1 1
.... ...x     | 0 0 0 2 | * * * * * * * * * 3 | 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 | 0 1 0 1 0 0 1
--------------+---------+---------------------+-------------------------------+--------------
x...3o...     | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * | 1 1 0 0 0 0 0
xo.. ....&#x  | 2 1 0 0 | 1 2 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * | 1 0 1 0 0 0 0
.... ox..&#x  | 1 2 0 0 | 0 2 0 1 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * | 1 0 0 1 0 0 0
x..x ....&#x  | 2 0 0 2 | 1 0 2 0 0 0 0 0 1 0 | * * * 3 * * * * * * * * * * * | 0 1 1 0 0 0 0
.... o..x&#x  | 1 0 0 2 | 0 0 2 0 0 0 0 0 0 1 | * * * * 3 * * * * * * * * * * | 0 1 0 1 0 0 0
oo.o3oo.o&#x  | 1 1 0 1 | 0 1 1 0 0 1 0 0 0 0 | * * * * * 6 * * * * * * * * * | 0 0 1 1 0 0 0
.o..3.x..     | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 0 | * * * * * * 1 * * * * * * * * | 1 0 0 0 1 0 0
.ox. ....&#x  | 0 1 2 0 | 0 0 0 0 2 0 1 0 0 0 | * * * * * * * 3 * * * * * * * | 0 0 0 0 1 1 0
.... .xo.&#x  | 0 2 1 0 | 0 0 0 1 2 0 0 0 0 0 | * * * * * * * * 3 * * * * * * | 0 0 0 1 1 0 0
.o.x ....&#x  | 0 1 0 2 | 0 0 0 0 0 2 0 0 1 0 | * * * * * * * * * 3 * * * * * | 0 0 1 0 0 1 0
.ooo3.ooo&#x  | 0 1 1 1 | 0 0 0 0 1 1 0 1 0 0 | * * * * * * * * * * 6 * * * * | 0 0 0 1 0 1 0
..x.3..o.     | 0 0 3 0 | 0 0 0 0 0 0 3 0 0 0 | * * * * * * * * * * * 1 * * * | 0 0 0 0 1 0 1
..xx ....&#x  | 0 0 2 2 | 0 0 0 0 0 0 1 2 1 0 | * * * * * * * * * * * * 3 * * | 0 0 0 0 0 1 1
.... ..ox&#x  | 0 0 1 2 | 0 0 0 0 0 0 0 2 0 1 | * * * * * * * * * * * * * 3 * | 0 0 0 1 0 0 1
...x3...x     | 0 0 0 6 | 0 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * * * * 1 | 0 1 0 0 0 0 1
--------------+---------+---------------------+-------------------------------+--------------
xo..3ox..&#x  ♦ 3 3 0 0 | 3 6 0 3 0 0 0 0 0 0 | 1 3 3 0 0 0 1 0 0 0 0 0 0 0 0 | 1 * * * * * *
x..x3o..x&#x  ♦ 3 0 0 6 | 3 0 6 0 0 0 0 0 3 3 | 1 0 0 3 3 0 0 0 0 0 0 0 0 0 1 | * 1 * * * * *
xo.x ....&#x  ♦ 2 1 0 2 | 1 2 2 0 0 2 0 0 1 0 | 0 1 0 1 0 2 0 0 0 1 0 0 0 0 0 | * * 3 * * * *
.... oxox&#xr ♦ 1 2 1 2 | 0 2 2 1 2 2 0 2 0 1 | 0 0 1 0 1 2 0 0 1 0 2 0 0 1 0 | * * * 3 * * *
.ox.3.xo.&#x  ♦ 0 3 3 0 | 0 0 0 3 6 0 3 0 0 0 | 0 0 0 0 0 0 1 3 3 0 0 1 0 0 0 | * * * * 1 * *
.oxx ....&#x  ♦ 0 1 2 2 | 0 0 0 0 2 2 1 2 1 0 | 0 0 0 0 0 0 0 1 0 1 2 0 1 0 0 | * * * * * 3 *
..xx3..ox&#x  ♦ 0 0 3 6 | 0 0 0 0 0 0 3 6 3 3 | 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1 | * * * * * * 1