| Acronym | ... |
| Name | tetracontoctachoron-derived Gévay polychoron |
| Circumradius | ... |
| Face vector | 528, 2496, 2880, 912 |
| Confer |
|
This polychoron was designed to be a non-Wythoffian example within the class of perfect polytopes. Perfect polytopes by definition do not allow for variations without changing the action of its symmetry group on its face-lattice.
This specific case was derived from cont by placing smaller rads into its tics in such a way, that one class of its vertices becomes coincident to their octagon face centers, while the other class would be internal. The full polytope then is nothing but the convex hull of the so far obtained substructure.
All b and c edges, provided in the below description, only qualify as pseudo edges wrt. the full polychoron.
The rhombs {(r,R)2} have vertex angles r = arccos(1/3) = 70.528779° resp. R = arccos(-1/3) = 109.471221°. Esp. rr : RR = sqrt(2).
Incidence matrix according to Dynkin symbol
aco3boo4oob3oca&#z(x,x,d) → heights = 0
lacing(1,2) = lacing(2,3) = x
lacing(1,3) = d
a = (sqrt(8)-1)/sqrt(3) = 1.055643
b = 2/sqrt(3) = 1.154701
c = sqrt(8/3) = 1.632993
d = sqrt[(6-sqrt(2))/3] = 1.236364
(tegum sum of 2 mutually inverted (a,b)-ticoes and an a-spic)
o..3o..4o..3o.. | 192 * * | 1 3 6 0 0 | 3 6 3 6 0 | 1 3 3 3 0
.o.3.o.4.o.3.o. | * 144 * | 0 4 0 4 0 | 4 0 0 8 4 | 1 0 4 4 1
..o3..o4..o3..o | * * 192 | 0 0 6 3 1 | 0 3 6 6 3 | 0 3 3 3 1
--------------------------+-------------+--------------------+----------------------+------------------
a.. ... ... ... | 2 0 0 | 96 * * * * | 0 6 0 0 0 | 0 3 3 0 0 a
oo.3oo.4oo.3oo.&#x | 1 1 0 | * 576 * * * | 2 0 0 2 0 | 1 0 1 2 0 x
o.o3o.o4o.o3o.o&#d | 1 0 1 | * * 1152 * * | 0 1 1 1 0 | 0 1 1 1 0 d
.oo3.oo4.oo3.oo&#x | 0 1 1 | * * * 576 * | 0 0 0 2 2 | 0 0 2 1 1 x
... ... ... ..a | 0 0 2 | * * * * 96 | 0 0 6 0 0 | 0 3 0 3 0 a
--------------------------+-------------+--------------------+----------------------+------------------
... bo. ... oc.&#zx | 2 2 0 | 0 4 0 0 0 | 288 * * * * | 1 0 0 1 0 {(r,R)2}
a.o ... ... ...&#d | 2 0 1 | 1 0 2 0 0 | * 576 * * * | 0 1 1 0 0 add
... ... ... o.a&#d | 1 0 2 | 0 0 2 0 1 | * * 576 * * | 0 1 0 1 0 add
ooo3ooo4ooo3ooo&#r(x,x,d) | 1 1 1 | 0 1 1 1 0 | * * * 1152 * | 0 0 1 1 0 xxd
.co ... .ob ...&#zx | 0 2 2 | 0 0 0 4 0 | * * * * 288 | 0 0 1 0 1 {(r,R)2}
--------------------------+-------------+--------------------+----------------------+------------------
... bo.4oo.3oc.&#zx | 8 6 0 | 0 24 0 0 0 | 12 0 0 0 0 | 24 * * * * rad
a.o ... ... o.a&#d | 2 0 2 | 1 0 4 0 1 | 0 2 2 0 0 | * 288 * * * (a,d)-2ap
aco ... oob ...&#(x,zx,d) | 2 2 2 | 1 2 4 4 0 | 0 2 0 4 1 | * * 288 * * "rhomb wedge"
... boo ... oca&#(zx,x,d) | 2 2 2 | 0 4 4 2 1 | 1 0 2 4 0 | * * * 288 * "rhomb wedge"
.co3.oo4.ob ...&#zx | 0 6 8 | 0 0 0 24 0 | 0 0 0 0 12 | * * * * 24 rad
or
o..3o..4o..3o.. & | 384 * | 1 3 6 | 3 9 6 | 1 3 6
.o.3.o.4.o.3.o. | * 144 | 0 8 0 | 8 0 8 | 2 0 8
----------------------------+---------+---------------+---------------+-----------
a.. ... ... ... & | 2 0 | 192 * * | 0 6 0 | 0 3 3 a
oo.3oo.4oo.3oo.&#x & | 1 1 | * 1152 * | 2 0 2 | 1 0 3 x
o.o3o.o4o.o3o.o&#d | 2 0 | * * 1152 | 0 2 1 | 0 1 2 d
----------------------------+---------+---------------+---------------+-----------
... bo. ... oc.&#zx & | 2 2 | 0 4 0 | 576 * * | 1 0 1 {(r,R)2}
a.o ... ... ...&#d & | 3 0 | 1 0 2 | * 1152 * | 0 1 1 add
ooo3ooo4ooo3ooo&#r(x,x,d) | 2 1 | 0 2 1 | * * 1152 | 0 0 2 xxd
----------------------------+---------+---------------+---------------+-----------
... bo.4oo.3oc.&#zx & | 8 6 | 0 24 0 | 12 0 0 | 48 * * rad
a.o ... ... o.a&#d | 4 0 | 2 0 4 | 0 4 0 | * 288 * (a,d)-2ap
aco ... oob ...&#(x,zx,d) & | 4 2 | 1 6 4 | 1 2 4 | * * 576 "rhomb wedge"
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