Acronym cute (old: cubdipy)
Name cubical (line-)tegum,
cubical bipyramid
Circumradius ...
Dual ope
Dihedral angles
Confer
segmentochora:
cubpy   squasc  
uniform relative:
ico  
general polytopal classes:
isohedral polytope   n-prismatic bipyramids   bistratic lace towers  

Just as ico can be decomposed into 8 cubdipy according to ooq3ooo3ooo4oxo&#zx, so also cute itself can either be decomposed equatorially into 2 cubpy or alternatively, kind like a 4D orange, into 6 squascs. (The blend of these 2 decompositions of cute, blending out out the boundary cells of cute, then would be the degenerate 5D segmentoteron cubasc.)


Incidence matrix according to Dynkin symbol

ooo3ooo4oxo&#xt   → both heights = 1/2
(pt || pseudo cube || pt)

o..3o..4o..    | 1 * *  8  0 0 | 12 0  0 | 6 0
.o.3.o.4.o.    | * 8 * | 1  3 1 |  3 3  3 | 3 3
..o3..o4..o    | * * 1  0  0 8 |  0 0 12 | 0 6
---------------+-------+--------+---------+----
oo.3oo.4oo.&#x | 1 1 0 | 8  * * |  3 0  0 | 3 0
... ... .x.    | 0 2 0 | * 12 * |  1 2  1 | 2 2
.oo3.oo4.oo&#x | 0 1 1 | *  * 8 |  0 0  3 | 0 3
---------------+-------+--------+---------+----
... ... ox.&#x | 1 2 0 | 2  1 0 | 12 *  * | 2 0
... .o.4.x.    | 0 4 0 | 0  4 0 |  * 6  * | 1 1
... ... .xo&#x | 0 2 1 | 0  1 2 |  * * 12 | 0 2
---------------+-------+--------+---------+----
... oo.4ox.&#x  1 4 0 | 4  4 0 |  4 1  0 | 6 *
... .oo4.xo&#x  0 4 1 | 0  4 4 |  0 1  4 | * 6

xo oo3oo4ox&#zx   → height = 0
(tegum product of pseudo line with cube)

o. o.3o.4o.    | 2 *   8  0 | 12 0 |  6
.o .o3.o4.o    | * 8 |  2  3 |  6 3 |  6
---------------+-----+-------+------+---
oo oo3oo4oo&#x | 1 1 | 16  * |  3 0 |  3
.. .. .. .x    | 0 2 |  * 12 |  2 2 |  4
---------------+-----+-------+------+---
.. .. .. ox&#x | 1 2 |  2  1 | 24 * |  2
.. .. .o4.x    | 0 4 |  0  4 |  * 6 |  2
---------------+-----+-------+------+---
.. .. oo4ox&#x  1 4 |  4  4 |  4 1 | 12

oxo oxo4ooo&#xt   → both heights = 1/2
(pt || pseudo cube || pt)

o.. o..4o..    & | 2 *   8 0 0 | 4  8 0 0 | 4 2
.o. .o. .o.      | * 8 |  2 1 2 | 2  4 2 1 | 4 2
-----------------+-----+--------+----------+----
oo. oo.4oo.&#x & | 1 1 | 16 * * | 1  2 0 0 | 2 1
.x. ... ...      | 0 2 |  * 4 * | 2  0 2 0 | 4 0
... .x. ...      | 0 2 |  * * 8 | 0  2 1 1 | 2 2
-----------------+-----+--------+----------+----
ox. ... ...&#x & | 1 2 |  2 1 0 | 8  * * * | 2 0
... ox. ...&#x & | 1 2 |  2 0 1 | * 16 * * | 1 1
.x. .x. ...      | 0 4 |  0 2 2 | *  * 4 * | 2 0
... .x.4.o.      | 0 4 |  0 0 4 | *  * * 2 | 0 2
-----------------+-----+--------+----------+----
ox. ox. ...&#x &  1 4 |  4 2 2 | 2  2 1 0 | 8 *
... ox.4oo.&#x &  1 4 |  4 0 4 | 0  4 0 1 | * 4

oxo oxo oxo&#xt   → both heights = 1/2
(pt || pseudo cube || pt)

o.. o.. o..    | 1 * *  8 0 0 0 0 | 4 4 4 0 0 0 0 0 0 | 2 2 2 0 0 0
.o. .o. .o.    | * 8 * | 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 1
..o ..o ..o    | * * 1  0 0 0 0 8 | 0 0 0 0 0 0 4 4 4 | 0 0 0 2 2 2
---------------+-------+-----------+-------------------+------------
oo. oo. oo.&#x | 1 1 0 | 8 * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 0
.x. ... ...    | 0 2 0 | * 4 * * * | 1 0 0 1 1 0 1 0 0 | 1 1 0 1 1 0
... .x. ...    | 0 2 0 | * * 4 * * | 0 1 0 1 0 1 0 1 0 | 1 0 1 1 0 1
... ... .x.    | 0 2 0 | * * * 4 * | 0 0 1 0 1 1 0 0 1 | 0 1 1 0 1 1
.oo .oo .oo&#x | 0 1 1 | * * * * 8 | 0 0 0 0 0 0 1 1 1 | 0 0 0 1 1 1
---------------+-------+-----------+-------------------+------------
ox. ... ...&#x | 1 2 0 | 2 1 0 0 0 | 4 * * * * * * * * | 1 1 0 0 0 0
... ox. ...&#x | 1 2 0 | 2 0 1 0 0 | * 4 * * * * * * * | 1 0 1 0 0 0
... ... ox.&#x | 1 2 0 | 2 0 0 1 0 | * * 4 * * * * * * | 0 1 1 0 0 0
.x. .x. ...    | 0 4 0 | 0 2 2 0 0 | * * * 2 * * * * * | 1 0 0 1 0 0
.x. ... .x.    | 0 4 0 | 0 2 0 2 0 | * * * * 2 * * * * | 0 1 0 0 1 0
... .x. .x.    | 0 4 0 | 0 0 2 2 0 | * * * * * 2 * * * | 0 0 1 0 0 1
.xo ... ...&#x | 0 2 1 | 0 1 0 0 2 | * * * * * * 4 * * | 0 0 0 1 1 0
... .xo ...&#x | 0 2 1 | 0 0 1 0 2 | * * * * * * * 4 * | 0 0 0 1 0 1
... ... .xo&#x | 0 2 1 | 0 0 0 1 2 | * * * * * * * * 4 | 0 0 0 0 1 1
---------------+-------+-----------+-------------------+------------
ox. ox. ...&#x  1 4 0 | 4 2 2 0 0 | 2 2 0 1 0 0 0 0 0 | 2 * * * * *
ox. ... ox.&#x  1 4 0 | 4 2 0 2 0 | 2 0 2 0 1 0 0 0 0 | * 2 * * * *
... ox. ox.&#x  1 4 0 | 4 0 2 2 0 | 0 2 2 0 0 1 0 0 0 | * * 2 * * *
.xo .xo ...&#x  0 4 1 | 0 2 2 0 4 | 0 0 0 1 0 0 2 2 0 | * * * 2 * *
.xo ... .xo&#x  0 4 1 | 0 2 0 2 4 | 0 0 0 0 1 0 2 0 2 | * * * * 2 *
... .xo .xo&#x  0 4 1 | 0 0 2 2 4 | 0 0 0 0 0 1 0 2 2 | * * * * * 2

oxo xox4ooo&#xt   → both heights = 1/2
({4} || pseudo ortho line || {4})

o.. o.. o..    & | 8 * | 2  2 1 | 1  4 2 2 | 2 4
.o. .o. .o.      | * 2  0  8 0 | 0  8 0 4 | 2 4
-----------------+-----+--------+----------+----
... x.. ...    & | 2 0 | 8  * * | 1  2 1 0 | 2 2
oo. oo.4oo.&#x & | 1 1 | * 16 * | 0  2 0 1 | 1 2
o.o o.o4o.o&#x   | 2 0 | *  * 4 | 0  0 2 2 | 0 4
-----------------+-----+--------+----------+----
... x..4o..    & | 4 0 | 4  0 0 | 2  * * * | 2 0
... xo. ...&#x & | 2 1 | 1  2 0 | * 16 * * | 1 1
... x.x ...&#x   | 4 0 | 2  0 2 | *  * 4 * | 0 2
ooo ooo4ooo&#x   | 2 1 | 0  2 1 | *  * * 8 | 0 2
-----------------+-----+--------+----------+----
... xo.4oo.&#x &  4 1 | 4  4 0 | 1  4 0 0 | 4 *
... xox ...&#x    4 1 | 2  4 2 | 0  2 1 2 | * 8

oxo xox xox&#xt   → both heights = 1/2
({4} || pseudo ortho line || {4})

o.. o.. o..    | 4 * * | 1 1 2 1 0 0 0 | 1 2 2 1 1 2 0 0 0 | 2 2 2 0
.o. .o. .o.    | * 2 *  0 0 4 0 4 0 0 | 0 2 2 0 0 4 2 2 0 | 1 2 2 1
..o ..o ..o    | * * 4 | 0 0 0 1 2 1 1 | 0 0 0 1 1 2 2 2 1 | 0 2 2 2
---------------+-------+---------------+-------------------+--------
... x.. ...    | 2 0 0 | 2 * * * * * * | 1 2 0 1 0 0 0 0 0 | 2 2 0 0
... ... x..    | 2 0 0 | * 2 * * * * * | 1 0 2 0 1 0 0 0 0 | 2 0 2 0
oo. oo. oo.&#x | 1 1 0 | * * 8 * * * * | 0 1 1 0 0 1 0 0 0 | 1 1 1 0
o.o o.o o.o&#x | 1 0 1 | * * * 4 * * * | 0 0 0 1 1 2 0 0 0 | 0 2 2 0
.oo .oo .oo&#x | 0 1 1 | * * * * 8 * * | 0 0 0 0 0 1 1 1 0 | 0 1 1 1
... ..x ...    | 0 0 2 | * * * * * 2 * | 0 0 0 1 0 0 2 0 1 | 0 2 0 2
... ... ..x    | 0 0 2 | * * * * * * 2 | 0 0 0 0 1 0 0 2 1 | 0 0 2 2
---------------+-------+---------------+-------------------+--------
... x.. x..    | 4 0 0 | 2 2 0 0 0 0 0 | 1 * * * * * * * * | 2 0 0 0
... xo. ...&#x | 2 1 0 | 1 0 2 0 0 0 0 | * 4 * * * * * * * | 1 1 0 0
... ... xo.&#x | 2 1 0 | 0 1 2 0 0 0 0 | * * 4 * * * * * * | 1 0 1 0
... x.x ...&#x | 2 0 2 | 1 0 0 2 0 1 0 | * * * 2 * * * * * | 0 2 0 0
... ... x.x&#x | 2 0 2 | 0 1 0 2 0 0 1 | * * * * 2 * * * * | 0 0 2 0
ooo ooo ooo&#x | 1 1 1 | 0 0 1 1 1 0 0 | * * * * * 8 * * * | 0 1 1 0
... .ox ...&#x | 0 1 2 | 0 0 0 0 2 1 0 | * * * * * * 4 * * | 0 1 0 1
... ... .ox&#x | 0 1 2 | 0 0 0 0 2 0 1 | * * * * * * * 4 * | 0 0 1 1
... ..x ..x    | 0 0 4 | 0 0 0 0 0 2 2 | * * * * * * * * 1 | 0 0 0 2
---------------+-------+---------------+-------------------+--------
... xo. xo.&#x  4 1 0 | 2 2 4 0 0 0 0 | 1 2 2 0 0 0 0 0 0 | 2 * * *
... xox ...&#x  2 1 2 | 1 0 2 2 2 1 0 | 0 1 0 1 0 2 1 0 0 | * 4 * *
... ... xox&#x  2 1 2 | 0 1 2 2 2 0 1 | 0 0 1 0 1 2 0 1 0 | * * 4 *
... .ox .ox&#x  0 1 4 | 0 0 0 0 4 2 2 | 0 0 0 0 0 0 2 2 1 | * * * 2

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