Acronym | ... |
Name |
q x4o, variation of cube, vertex figure of rectified cubic honeycomb |
Circumradius | 1 |
Lace city in approx. ASCII-art |
x x x x |
q q q q | |
o q o o q o | |
Volume | sqrt(2) = 1.414214 |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dihedral angles |
|
Face vector | 8, 12, 6 |
Confer |
using edge sizes x = 1 and q = sqrt(2) = 1.414214
Incidence matrix according to Dynkin symbol
q x4o . . . | 8 | 1 2 | 2 1 ------+---+-----+---- q . . | 2 | 4 * | 2 0 . x . | 2 | * 8 | 1 1 ------+---+-----+---- q x . | 4 | 2 2 | 4 * . x4o | 4 | 0 4 | * 2
q x x . . . | 8 | 1 1 1 | 1 1 1 ------+---+-------+------ q . . | 2 | 4 * * | 1 1 0 . x . | 2 | * 4 * | 1 0 1 . . x | 2 | * * 4 | 0 1 1 ------+---+-------+------ q x . | 4 | 2 2 0 | 2 * * q . x | 4 | 2 0 2 | * 2 * . x x | 4 | 0 2 2 | * * 2
xx4oo&#q → height = sqrt(2) = 1.414214
({4} || {4})
o.4o. | 4 * | 2 1 0 | 1 2 0
.o4.o | * 4 | 0 1 2 | 0 2 1
---------+-----+-------+------
x. .. | 2 0 | 4 * * | 1 1 0
oo4oo&#q | 1 1 | * 4 * | 0 2 0
.x .. | 0 2 | * * 4 | 0 1 1
---------+-----+-------+------
x.4o. | 4 0 | 4 0 0 | 1 * *
xx ..&#q | 2 2 | 1 2 1 | * 4 *
.x4.o | 0 4 | 0 0 4 | * * 1
xx xx&#q → height = sqrt(2) = 1.414214
({4} || {4})
o. o. | 4 * | 1 1 1 0 0 | 1 1 1 0
.o .o | * 4 | 0 0 1 1 1 | 0 1 1 1
---------+-----+-----------+--------
x. .. | 2 0 | 2 * * * * | 1 1 0 0
.. x. | 2 0 | * 2 * * * | 1 0 1 0
oo oo&#q | 1 1 | * * 4 * * | 0 1 1 0
.x .. | 0 2 | * * * 2 * | 0 1 0 1
.. .x | 0 2 | * * * * 2 | 0 0 1 1
---------+-----+-----------+--------
x. x. | 4 0 | 2 2 0 0 0 | 1 * * *
xx ..&#q | 2 2 | 1 0 2 1 0 | * 2 * *
.. xx&#q | 2 2 | 0 1 2 0 1 | * * 2 *
.x .x | 0 4 | 0 0 0 2 2 | * * * 1
qq xx&#x → height = 1
((q,x)-{4} || (q,x)-{4})
o. o. | 4 * | 1 1 1 0 0 | 1 1 1 0
.o .o | * 4 | 0 0 1 1 1 | 0 1 1 1
---------+-----+-----------+--------
q. .. | 2 0 | 2 * * * * | 1 1 0 0
.. x. | 2 0 | * 2 * * * | 1 0 1 0
oo oo&#x | 1 1 | * * 4 * * | 0 1 1 0
.q .. | 0 2 | * * * 2 * | 0 1 0 1
.. .x | 0 2 | * * * * 2 | 0 0 1 1
---------+-----+-----------+--------
q. x. | 4 0 | 2 2 0 0 0 | 1 * * *
qq ..&#x | 2 2 | 1 0 2 1 0 | * 2 * *
.. xx&#x | 2 2 | 0 1 2 0 1 | * * 2 *
.q .x | 0 4 | 0 0 0 2 2 | * * * 1
qqq oqo&#xt → both heights = 1/sqrt(2) = 0.707107 (q-line || pseudo q-{4} || q-line) o.. o.. | 2 * * | 1 2 0 0 0 | 2 1 0 .o. .o. | * 4 * | 0 1 1 1 0 | 1 1 1 ..o ..o | * * 2 | 0 0 0 2 1 | 0 1 2 ------------+-------+-----------+------ q.. ... | 2 0 0 | 1 * * * * | 2 0 0 oo. oo.&#x | 1 1 0 | * 4 * * * | 1 1 0 .q. ... | 0 2 0 | * * 2 * * | 1 0 1 .oo .oo&#x | 0 1 1 | * * * 4 * | 0 1 1 ..q ... | 0 0 2 | * * * * 1 | 0 0 2 ------------+-------+-----------+------ qq. ...&#x | 2 2 0 | 1 2 1 0 0 | 2 * * ... oqo&#xt | 1 2 1 | 0 2 0 2 0 | * 2 * .qq ...&#x | 0 2 2 | 0 0 1 2 1 | * * 2
or o.. o.. & | 4 * | 1 2 0 | 2 1 .o. .o. | * 4 | 0 2 1 | 2 1 ---------------+-----+-------+---- q.. ... & | 2 0 | 2 * * | 2 0 oo. oo.&#x & | 1 1 | * 8 * | 1 1 .q. ... | 0 2 | * * 2 | 2 0 ---------------+-----+-------+---- qq. ...&#x & | 2 2 | 1 2 1 | 4 * ... oqo&#xt | 2 2 | 0 4 0 | * 2
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