squacupe

Acronym	squacupe, K-4.69
Name	square-cupola prism, cube atop octagonal prism
Segmentochoron display
Circumradius	sqrt[(3+sqrt(2))/2] = 1.485633
Lace city in approx. ASCII-art	x4o x4x -- squacu x4o x4x -- squacu \| +- op +------ cube
Volume	[3+2 sqrt(2)]/3 = 1.942809
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Face vector	24, 52, 40, 12
Confer	more general: n/d-cupe uniform relative: sircope sidpith general polytopal classes: segmentochora
External links

Incidence matrix according to Dynkin symbol

xx4ox xx&#x   → height = 1/sqrt(2) = 0.707107
(cube || op)

o.4o. o.    | 8  * | 2 1  2 0 0 0 | 1 2 2 1 2 0 0 0 | 1 1 2 1 0
.o4.o .o    | * 16 | 0 0  1 1 1 1 | 0 0 1 1 1 1 1 1 | 0 1 1 1 1
------------+------+--------------+-----------------+----------
x. .. ..    | 2  0 | 8 *  * * * * | 1 1 1 0 0 0 0 0 | 1 1 1 0 0
.. .. x.    | 2  0 | * 4  * * * * | 0 2 0 0 2 0 0 0 | 1 0 2 1 0
oo4oo oo&#x | 1  1 | * * 16 * * * | 0 0 1 1 1 0 0 0 | 0 1 1 1 0
.x .. ..    | 0  2 | * *  * 8 * * | 0 0 1 0 0 1 1 0 | 0 1 1 0 1
.. .x ..    | 0  2 | * *  * * 8 * | 0 0 0 1 0 1 0 1 | 0 1 0 1 1
.. .. .x    | 0  2 | * *  * * * 8 | 0 0 0 0 1 0 1 1 | 0 0 1 1 1
------------+------+--------------+-----------------+----------
x.4o. ..    | 4  0 | 4 0  0 0 0 0 | 2 * * * * * * * | 1 1 0 0 0
x. .. x.    | 4  0 | 2 2  0 0 0 0 | * 4 * * * * * * | 1 0 1 0 0
xx .. ..&#x | 2  2 | 1 0  2 1 0 0 | * * 8 * * * * * | 0 1 1 0 0
.. ox ..&#x | 1  2 | 0 0  2 0 1 0 | * * * 8 * * * * | 0 1 0 1 0
.. .. xx&#x | 2  2 | 0 1  2 0 0 1 | * * * * 8 * * * | 0 0 1 1 0
.x4.x ..    | 0  8 | 0 0  0 4 4 0 | * * * * * 2 * * | 0 1 0 0 1
.x .. .x    | 0  4 | 0 0  0 2 0 2 | * * * * * * 4 * | 0 0 1 0 1
.. .x .x    | 0  4 | 0 0  0 0 2 2 | * * * * * * * 4 | 0 0 0 1 1
------------+------+--------------+-----------------+----------
x.4o. x.    ♦ 8  0 | 8 4  0 0 0 0 | 2 4 0 0 0 0 0 0 | 1 * * * *
xx4ox ..&#x ♦ 4  8 | 4 0  8 4 4 0 | 1 0 3 3 0 1 0 0 | * 2 * * *
xx .. xx&#x ♦ 4  4 | 2 2  4 2 0 2 | 0 1 2 0 2 0 1 0 | * * 4 * *
.. ox xx&#x ♦ 2  4 | 0 1  4 0 2 2 | 0 0 0 2 2 0 0 1 | * * * 4 *
.x4.x .x    ♦ 0 16 | 0 0  0 8 8 8 | 0 0 0 0 0 2 4 4 | * * * * 1

xx4ox&#x || xx4ox&#x   → height = 1
(squacu || squacu)

o.4o.    || .. ..    | 4 * * * | 2 2 1 0 0 0 0 0 0 0 | 1 2 1 2 2 0 0 0 0 0 0 0 | 1 1 2 1 0 0
.o4.o    || .. ..    | * 8 * * | 0 1 0 1 1 1 0 0 0 0 | 0 1 1 0 1 1 1 1 0 0 0 0 | 1 0 1 1 1 0
.. ..    || o.4o.    | * * 4 * | 0 0 1 0 0 0 2 2 0 0 | 0 0 0 2 2 0 0 0 1 2 1 0 | 0 1 2 1 0 1
.. ..    || .o4.o    | * * * 8 | 0 0 0 0 0 1 0 1 1 1 | 0 0 0 0 1 0 1 1 0 1 1 1 | 0 0 1 1 1 1
---------------------+---------+---------------------+-------------------------+------------
x. ..    || .. ..    | 2 0 0 0 | 4 * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
oo4oo&#x || .. ..    | 1 1 0 0 | * 8 * * * * * * * * | 0 1 1 0 1 0 0 0 0 0 0 0 | 1 0 1 1 0 0
o.4o.    || o.4o.    | 1 0 1 0 | * * 4 * * * * * * * | 0 0 0 2 2 0 0 0 0 0 0 0 | 0 1 2 1 0 0
.x ..    || .. ..    | 0 2 0 0 | * * * 4 * * * * * * | 0 1 0 0 0 1 1 0 0 0 0 0 | 1 0 1 0 1 0
.. .x    || .. ..    | 0 2 0 0 | * * * * 4 * * * * * | 0 0 1 0 0 1 0 1 0 0 0 0 | 1 0 0 1 1 0
.o4.o    || .o4.o    | 0 1 0 1 | * * * * * 8 * * * * | 0 0 0 0 1 0 1 1 0 0 0 0 | 0 0 1 1 1 0
.. ..    || x. ..    | 0 0 2 0 | * * * * * * 4 * * * | 0 0 0 1 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
.. ..    || oo4oo&#x | 0 0 1 1 | * * * * * * * 8 * * | 0 0 0 0 1 0 0 0 0 1 1 0 | 0 0 1 1 0 1
.. ..    || .x ..    | 0 0 0 2 | * * * * * * * * 4 * | 0 0 0 0 0 0 1 0 0 1 0 1 | 0 0 1 0 1 1
.. ..    || .. .x    | 0 0 0 2 | * * * * * * * * * 4 | 0 0 0 0 0 0 0 1 0 0 1 1 | 0 0 0 1 1 1
---------------------+---------+---------------------+-------------------------+------------
x.4o.    || .. ..    | 4 0 0 0 | 4 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * | 1 1 0 0 0 0
xx ..&#x || .. ..    | 2 2 0 0 | 1 2 0 1 0 0 0 0 0 0 | * 4 * * * * * * * * * * | 1 0 1 0 0 0
.. ox&#x || .. ..    | 1 2 0 0 | 0 2 0 0 1 0 0 0 0 0 | * * 4 * * * * * * * * * | 1 0 0 1 0 0
x. ..    || x. ..    | 2 0 2 0 | 1 0 2 0 0 0 1 0 0 0 | * * * 4 * * * * * * * * | 0 1 1 0 0 0
oo4oo&#x || oo4oo&#x | 1 1 1 1 | 0 1 1 0 0 1 0 1 0 0 | * * * * 8 * * * * * * * | 0 0 1 1 0 0
.x4.x    || .. ..    | 0 8 0 0 | 0 0 0 4 4 0 0 0 0 0 | * * * * * 1 * * * * * * | 1 0 0 0 1 0
.x ..    || .x ..    | 0 2 0 2 | 0 0 0 1 0 2 0 0 1 0 | * * * * * * 4 * * * * * | 0 0 1 0 1 0
.. .x    || .. .x    | 0 2 0 2 | 0 0 0 0 1 2 0 0 0 1 | * * * * * * * 4 * * * * | 0 0 0 1 1 0
.. ..    || x.4o.    | 0 0 4 0 | 0 0 0 0 0 0 4 0 0 0 | * * * * * * * * 1 * * * | 0 1 0 0 0 1
.. ..    || xx ..&#x | 0 0 2 2 | 0 0 0 0 0 0 1 2 1 0 | * * * * * * * * * 4 * * | 0 0 1 0 0 1
.. ..    || .. ox&#x | 0 0 1 2 | 0 0 0 0 0 0 0 2 0 1 | * * * * * * * * * * 4 * | 0 0 0 1 0 1
.. ..    || .x4.x    | 0 0 0 8 | 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * * * 1 | 0 0 0 0 1 1
---------------------+---------+---------------------+-------------------------+------------
xx4ox&#x || .. ..    ♦ 4 8 0 0 | 4 8 0 4 4 0 0 0 0 0 | 1 4 4 0 0 1 0 0 0 0 0 0 | 1 * * * * *
x.4o.    || x.4o.    ♦ 4 0 4 0 | 4 0 4 0 0 0 4 0 0 0 | 1 0 0 4 0 0 0 0 1 0 0 0 | * 1 * * * *
xx ..&#x || xx ..&#x ♦ 2 2 2 2 | 1 2 2 1 0 2 1 2 1 0 | 0 1 0 1 2 0 1 0 0 1 0 0 | * * 4 * * *
.. ox&#x || .. ox&#x ♦ 1 2 1 2 | 0 2 1 0 1 2 0 2 0 1 | 0 0 1 0 2 0 0 1 0 0 1 0 | * * * 4 * *
.x4.x    || .x4.x    ♦ 0 8 0 8 | 0 0 0 4 4 8 0 0 4 4 | 0 0 0 0 0 1 4 4 0 0 0 1 | * * * * 1 *
.. ..    || xx4ox&#x ♦ 0 0 4 8 | 0 0 0 0 0 0 4 8 4 4 | 0 0 0 0 0 0 0 0 1 4 4 1 | * * * * * 1

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