Acronym ...
Name 4D corner hypercubera
Circumradius 1
Dual combinatorically self-dual
Confer
uniform relative:
tes  

The name cubera is a portmanteau of the words 'cube' and 'chimera'. The 3D cubera achieves its self-duality as the result of being, essentially, half cube and half octahedron (the dual polyhedron of a cube). In fact it has three square facets joined at a vertex (the cube 'half') and four triangles, with three of them adjoining a central triangle (the octahedron 'half').

Dan Moore found a general dimensional analogy thereof in its sense of an hypercubical-corner-simplex atop full-hypercube. Moreover, as also proved by him here, those (corner) hypercubera happen to be combinatorically dual in general!


Incidence matrix according to Dynkin symbol

oq3oo&#x || oqoo3ooqo&#xt   → height = 1
(where: x = 1, q = sqrt(2) = 1.414214, h = sqrt(3) = 1.732051)

o.3o.      .... ....     | 1 * * * * *  3 1 0 0 0 0 0 0 0 | 3 3 0 0 0 0 0 0 0 | 1 3 0 0 0 0  verf: q-tet
.o3.o      .... ....     | * 3 * * * * | 1 0 2 1 2 1 0 0 0 | 2 1 1 2 2 2 2 0 0 | 1 2 1 2 1 0
.. ..      o...3o...     | * * 1 * * * | 0 1 0 0 0 0 3 0 0 | 0 3 0 0 0 0 0 3 0 | 0 3 0 0 0 1
.. ..      .o..3.o..     | * * * 3 * * | 0 0 0 1 0 0 1 2 0 | 0 1 0 0 0 2 0 2 1 | 0 2 0 0 1 1
.. ..      ..o.3..o.     | * * * * 3 * | 0 0 0 0 2 0 0 2 1 | 0 0 0 1 0 2 2 1 2 | 0 1 0 1 2 1
.. ..      ...o3...o     | * * * * * 1  0 0 0 0 0 3 0 0 3 | 0 0 0 0 3 0 6 0 3 | 0 0 1 3 3 1  verf: q-oct
-------------------------+-------------+-------------------+-------------------+------------
oo3oo&#x   .... ....     | 1 1 0 0 0 0 | 3 * * * * * * * * | 2 1 0 0 0 0 0 0 0 | 1 2 0 0 0 0  x
o.3o.    || o...3o...     | 1 0 1 0 0 0 | * 1 * * * * * * * | 0 3 0 0 0 0 0 0 0 | 0 3 0 0 0 0  x
.q ..      .... ....     | 0 2 0 0 0 0 | * * 3 * * * * * * | 1 0 1 1 1 0 0 0 0 | 1 1 1 1 0 0  q
.o3.o    || .o..3.o..     | 0 1 0 1 0 0 | * * * 3 * * * * * | 0 1 0 0 0 2 0 0 0 | 0 2 0 0 1 0  x
.o3.o    || ..o.3..o.     | 0 1 0 0 1 0 | * * * * 6 * * * * | 0 0 0 1 0 1 1 0 0 | 0 1 0 1 1 0  q
.o3.o    || ...o3...o     | 0 1 0 0 0 1 | * * * * * 3 * * * | 0 0 0 0 2 0 2 0 0 | 0 0 1 2 1 0  h
.. ..      oo..3oo..&#x  | 0 0 1 1 0 0 | * * * * * * 3 * * | 0 1 0 0 0 0 0 2 0 | 0 2 0 0 0 1  x
.. ..      .oo.3.oo.&#x  | 0 0 0 1 1 0 | * * * * * * * 6 * | 0 0 0 0 0 1 0 1 1 | 0 1 0 0 1 1  x
.. ..      ..oo3..oo&#x  | 0 0 0 0 1 1 | * * * * * * * * 3 | 0 0 0 0 0 0 2 0 2 | 0 0 0 1 2 1  x
-------------------------+-------------+-------------------+-------------------+------------
oq ..&#x   .... ....     | 1 2 0 0 0 0 | 2 0 1 0 0 0 0 0 0 | 3 * * * * * * * * | 1 1 0 0 0 0
oo3oo&#x || oo..3oo..&#x  | 1 1 1 1 0 0 | 1 1 0 1 0 0 1 0 0 | * 3 * * * * * * * | 0 2 0 0 0 0
.q3.o      .... ....     | 0 3 0 0 0 0 | 0 0 3 0 0 0 0 0 0 | * * 1 * * * * * * | 1 0 1 0 0 0
.q ..    || ..o.3..o.     | 0 2 0 0 1 0 | 0 0 1 0 2 0 0 0 0 | * * * 3 * * * * * | 0 1 0 1 0 0
.q ..    || ...o3...o     | 0 2 0 0 0 1 | 0 0 1 0 0 2 0 0 0 | * * * * 3 * * * * | 0 0 1 1 0 0
.o3.o    || .oo.3.oo.&#x  | 0 1 0 1 1 0 | 0 0 0 1 1 0 0 1 0 | * * * * * 6 * * * | 0 1 0 0 1 0
.o3.o    || ..oo3..oo&#x  | 0 1 0 0 1 1 | 0 0 0 0 1 1 0 0 1 | * * * * * * 6 * * | 0 0 0 1 1 0
.. ..      oqo. ....&#xt | 0 0 1 2 1 0 | 0 0 0 0 0 0 2 2 0 | * * * * * * * 3 * | 0 1 0 0 0 1
.. ..      .... .oqo&#xt | 0 0 0 1 2 1 | 0 0 0 0 0 0 0 2 2 | * * * * * * * * 3 | 0 0 0 0 1 1
-------------------------+-------------+-------------------+-------------------+------------
oq3oo&#x   .... ....      1 3 0 0 0 0 | 3 0 3 0 0 0 0 0 0 | 3 0 1 0 0 0 0 0 0 | 1 * * * * *  top corner pyramid of cube
oq ..    || oqo. ....&#xt  1 2 1 2 1 0 | 2 1 1 2 2 0 2 2 0 | 1 2 0 1 0 2 0 1 0 | * 3 * * * *  cubera = half-square || square
.q3.o    || ...o3...o     | 0 3 0 0 0 1 | 0 0 3 0 0 3 0 0 0 | 0 0 1 0 3 0 0 0 0 | * * 1 * * *  straight q-{3} || pt
.q ..    || ..oo3..oo&#x  | 0 2 0 0 1 1 | 0 0 1 0 2 2 0 0 1 | 0 0 0 1 1 0 2 0 0 | * * * 3 * *  oblique q-line || x-line
.o3.o    || .... .oqo&#xt | 0 1 0 1 2 1 | 0 0 0 1 2 1 0 2 2 | 0 0 0 0 0 2 2 0 1 | * * * * 3 *  oblique pt || square
.. ..      oqoo3ooqo&#xt  0 0 1 3 3 1 | 0 0 0 0 0 0 3 6 3 | 0 0 0 0 0 0 0 3 3 | * * * * * 1  bottom full cube

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