Acronym quidex
Name quatro-icositetradiminished hexacosachoron,
dual of sadi
Vertex figures tet, doe
Dual sadi
Confer
uniform relative:
ex   sadi   hi  
segmentochora:
ikepy  
related scaliform:
bidex  
general polytopal classes:
subsymmetrical diminishings  

This one can be obtained by chopping off the 96 vertices of an ex, which correspond to 4 vertex-inscribed f-icoes. In fact 96 ikepies are to be cut off. But in contrast to sadi those ikepy would intersect here, resulting in titdi cells instead, which also show up some f-sized edges. – Quidex likewise can be obtained from sadi by chopping off the 72 vertices of 3 further vertex-inscribed f-icoes, or from bidex by diminishing at those of 2 such, resp. from those of tridex by diminishing at those of 1 such. Conversely it also can be considered as a subdimensional stellation of hi by apiculating 24 of the does within icoic positioning with pyramids of according heights. – For more details cf. here.


Incidence matrix according to Dynkin symbol

ooV|xoF|o-3-ooo|ooo|F-3-Voo|Fxo|o *b3-oVo|oFx|o-&#z(v,f,F)   → existing heights=0
                                                               V = 2f = 3.236068
                                                               F = ff = 2.618034

o.. ... .-3-o.. ... .-3-o.. ... . *b3-o.. ... .            | 8 * *  *  *  *  *   4  0  0  0  0  0  0 |  6  0  0  0  0  0 |  4  0  0
.o. ... .-3-.o. ... .-3-.o. ... . *b3-.o. ... .            | * 8 *  *  *  *  *   0  4  0  0  0  0  0 |  0  6  0  0  0  0 |  0  4  0
..o ... .-3-..o ... .-3-..o ... . *b3-..o ... .            | * * 8  *  *  *  *   0  0  4  0  0  0  0 |  0  0  6  0  0  0 |  0  0  4
... o.. .-3-... o.. .-3-... o.. . *b3-... o.. .            | * * * 32  *  *  *   1  0  0  3  0  0  0 |  3  0  0  3  0  0 |  3  0  1
... .o. .-3-... .o. .-3-... .o. . *b3-... .o. .            | * * *  * 32  *  *   0  1  0  0  3  0  0 |  0  3  0  0  3  0 |  1  3  0
... ..o .-3-... ..o .-3-... ..o . *b3-... ..o .            | * * *  *  * 32  *   0  0  1  0  0  3  0 |  0  0  3  0  0  3 |  0  1  3
... ... o-3-... ... o-3-... ... o *b3-... ... o            | * * *  *  *  * 24   0  0  0  4  4  4  8 |  2  2  2  8  8  8 |  4  4  4
-----------------------------------------------------------+-------------------+----------------------+-------------------+---------
o.. o.. .-3-o.. o.. .-3-o.. o.. . *b3-o.. o.. .-&#v        | 1 0 0  1  0  0  0 | 32  *  *  *  *  *  * |  3  0  0  0  0  0 |  3  0  0  v-edges
.o. .o. .-3-.o. .o. .-3-.o. .o. . *b3-.o. .o. .-&#v        | 0 1 0  0  1  0  0 |  * 32  *  *  *  *  * |  0  3  0  0  0  0 |  0  3  0  v-edges
..o ..o .-3-..o ..o .-3-..o ..o . *b3-..o ..o .-&#v        | 0 0 1  0  0  1  0 |  *  * 32  *  *  *  * |  0  0  3  0  0  0 |  0  0  3  v-edges
... o.. o-3-... o.. o-3-... o.. o *b3-... o.. o-&#f        | 0 0 0  1  0  0  1 |  *  *  * 96  *  *  * |  1  0  0  2  0  0 |  2  0  1  f-edges
... .o. o-3-... .o. o-3-... .o. o *b3-... .o. o-&#f        | 0 0 0  0  1  0  1 |  *  *  *  * 96  *  * |  0  1  0  0  2  0 |  1  2  0  f-edges
... ..o o-3-... ..o o-3-... ..o o *b3-... ..o o-&#f        | 0 0 0  0  0  1  1 |  *  *  *  *  * 96  * |  0  0  1  0  0  2 |  0  1  2  f-edges
... ... .   ... ... F   ... ... .     ... ... .            | 0 0 0  0  0  0  2 |  *  *  *  *  *  * 96 |  0  0  0  1  1  1 |  1  1  1  F-edges
-----------------------------------------------------------+-------------------+----------------------+-------------------+---------
o.. x.. o   ... ... .   ... ... .     ... ... .-&#(v,f)t   | 1 0 0  2  0  0  1 |  2  0  0  2  0  0  0 | 48  *  *  *  *  * |  2  0  0  kite
... ... .   ... ... .   .o. .x. o     ... ... .-&#(v,f)t   | 0 1 0  0  2  0  1 |  0  2  0  0  2  0  0 |  * 48  *  *  *  * |  0  2  0  kite
... ... .   ... ... .   ... ... .     ..o ..x o-&#(v,f)t   | 0 0 1  0  0  2  1 |  0  0  2  0  0  2  0 |  *  * 48  *  *  * |  0  0  2  kite
... ... .   ... o.. F   ... ... .     ... ... .-&#f        | 0 0 0  1  0  0  2 |  0  0  0  2  0  0  1 |  *  *  * 96  *  * |  1  0  1  golden triangle
... ... .   ... .o. F   ... ... .     ... ... .-&#f        | 0 0 0  0  1  0  2 |  0  0  0  0  2  0  1 |  *  *  *  * 96  * |  1  1  0  golden triangle
... ... .   ... ..o F   ... ... .     ... ... .-&#f        | 0 0 0  0  0  1  2 |  0  0  0  0  0  2  1 |  *  *  *  *  * 96 |  0  1  1  golden triangle
-----------------------------------------------------------+-------------------+----------------------+-------------------+---------
o.. xo. o-3-o.. oo. F   ... ... .     ... ... .-&#(v,f,f)t  1 0 0  3  1  0  3 |  3  0  0  6  3  0  3 |  3  0  0  3  3  0 | 32  *  *  tower a-d-g-e
... ... .   .o. .oo F-3-.o. .xo o     ... ... .-&#(v,f,f)t  0 1 0  0  3  1  3 |  0  3  0  0  6  3  3 |  0  3  0  0  3  3 |  * 32  *  tower b-e-g-f
... ... .   ..o o.o F   ... ... . *b3-..o o.x o-&#(v,f,f)t  0 0 1  1  0  3  3 |  0  0  3  3  0  6  3 |  0  0  3  3  0  3 |  *  * 32  tower c-f-g-d
or
o.. ... .-3-o.. ... .-3-o.. ... . *b3-o.. ... .            & | 24  *  *   4  0   0 |   6   0 |  4
... o.. .-3-... o.. .-3-... o.. . *b3-... o.. .            & |  * 96  *   1   3  0 |   3   3 |  4
... ... o-3-... ... o-3-... ... o *b3-... ... o              |  *  * 24   0  12  8 |   6  24 | 12
-------------------------------------------------------------+----------+-----------+---------+---
o.. o.. .-3-o.. o.. .-3-o.. o.. . *b3-o.. o.. .-&#v        & |  1  1  0 | 96   *  * |   3   0 |  3  v-edges
... o.. o-3-... o.. o-3-... o.. o *b3-... o.. o-&#f        & |  0  1  1 |  * 288  * |   1   2 |  3  f-edges
... ... .   ... ... F   ... ... .     ... ... .              |  0  0  2 |  *   * 96 |   0   3 |  3  F-edges
-------------------------------------------------------------+----------+-----------+---------+---
o.. x.. o   ... ... .   ... ... .     ... ... .-&#(v,f)t   & |  1  2  1 |  2   2  0 | 144   * |  2  kite
... ... .   ... o.. F   ... ... .     ... ... .-&#f        & |  0  1  2 |  0   2  1 |   * 288 |  2  golden triangle
-------------------------------------------------------------+----------+-----------+---------+---
o.. xo. o-3-o.. oo. F   ... ... .     ... ... .-&#(v,f,f)t &   1  4  3 |  3   9  3 |   3   6 | 96

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