Acronym | tisdip, K-4.18 |
Name |
triangle - square duoprism, square - cube wedge, vertex figure of nit |
|,>,O device | line pyramid prism prism = |>|| |
© © © | |
Circumradius | sqrt(5/6) = 0.912871 |
Coordinates |
|
Volume | sqrt(3)/4 = 0.433013 |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dihedral angles | |
Face vector | 12, 24, 19, 7 |
Confer |
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External links |
Incidence matrix according to Dynkin symbol
x3o x4o . . . . | 12 ♦ 2 2 | 1 4 1 | 2 2 --------+----+-------+--------+---- x . . . | 2 | 12 * | 1 2 0 | 2 1 . . x . | 2 | * 12 | 0 2 1 | 1 2 --------+----+-------+--------+---- x3o . . | 3 | 3 0 | 4 * * | 2 0 x . x . | 4 | 2 2 | * 12 * | 1 1 . . x4o | 4 | 0 4 | * * 3 | 0 2 --------+----+-------+--------+---- x3o x . ♦ 6 | 6 3 | 2 3 0 | 4 * x . x4o ♦ 8 | 4 8 | 0 4 2 | * 3
x x x3o . . . . | 12 ♦ 1 1 2 | 1 2 2 1 | 2 1 1 --------+----+--------+---------+------ x . . . | 2 | 6 * * | 1 2 0 0 | 2 1 0 . x . . | 2 | * 6 * | 1 0 2 0 | 2 0 1 . . x . | 2 | * * 12 | 0 1 1 1 | 1 1 1 --------+----+--------+---------+------ x x . . | 4 | 2 2 0 | 3 * * * | 2 0 0 x . x . | 4 | 2 0 2 | * 6 * * | 1 1 0 . x x . | 4 | 0 2 2 | * * 6 * | 1 0 1 . . x3o | 3 | 0 0 3 | * * * 4 | 0 1 1 --------+----+--------+---------+------ x x x . ♦ 8 | 4 4 4 | 2 2 2 0 | 3 * * x . x3o ♦ 6 | 3 0 6 | 0 3 0 2 | * 2 * . x x3o ♦ 6 | 0 3 6 | 0 0 3 2 | * * 2
x3o x4/3o . . . . | 12 ♦ 2 2 | 1 4 1 | 2 2 ----------+----+-------+--------+---- x . . . | 2 | 12 * | 1 2 0 | 2 1 . . x . | 2 | * 12 | 0 2 1 | 1 2 ----------+----+-------+--------+---- x3o . . | 3 | 3 0 | 4 * * | 2 0 x . x . | 4 | 2 2 | * 12 * | 1 1 . . x4/3o | 4 | 0 4 | * * 3 | 0 2 ----------+----+-------+--------+---- x3o x . ♦ 6 | 6 3 | 2 3 0 | 4 * x . x4/3o ♦ 8 | 4 8 | 0 4 2 | * 3
x3/2o x4o . . . . | 12 ♦ 2 2 | 1 4 1 | 2 2 ----------+----+-------+--------+---- x . . . | 2 | 12 * | 1 2 0 | 2 1 . . x . | 2 | * 12 | 0 2 1 | 1 2 ----------+----+-------+--------+---- x3/2o . . | 3 | 3 0 | 4 * * | 2 0 x . x . | 4 | 2 2 | * 12 * | 1 1 . . x4o | 4 | 0 4 | * * 3 | 0 2 ----------+----+-------+--------+---- x3/2o x . ♦ 6 | 6 3 | 2 3 0 | 4 * x . x4o ♦ 8 | 4 8 | 0 4 2 | * 3
x3/2o x4/3o . . . . | 12 ♦ 2 2 | 1 4 1 | 2 2 ------------+----+-------+--------+---- x . . . | 2 | 12 * | 1 2 0 | 2 1 . . x . | 2 | * 12 | 0 2 1 | 1 2 ------------+----+-------+--------+---- x3/2o . . | 3 | 3 0 | 4 * * | 2 0 x . x . | 4 | 2 2 | * 12 * | 1 1 . . x4/3o | 4 | 0 4 | * * 3 | 0 2 ------------+----+-------+--------+---- x3/2o x . ♦ 6 | 6 3 | 2 3 0 | 4 * x . x4/3o ♦ 8 | 4 8 | 0 4 2 | * 3
x4o s3s . . demi( . . ) | 12 ♦ 2 2 | 1 1 4 | 2 2 ----------------+----+-------+--------+---- x . demi( . . ) | 2 | 12 * | 1 0 2 | 1 2 . . sefa( s3s ) | 2 | * 12 | 0 1 2 | 2 1 ----------------+----+-------+--------+---- x4o demi( . . ) | 4 | 4 0 | 3 * * | 0 2 . . s3s ♦ 3 | 0 3 | * 4 * | 2 0 x . sefa( s3s ) | 4 | 2 2 | * * 12 | 1 1 ----------------+----+-------+--------+---- x . s3s ♦ 6 | 3 6 | 0 2 3 | 4 * x4o sefa( s3s ) ♦ 8 | 8 4 | 2 0 4 | * 3
x x s3s . . demi( . . ) | 12 ♦ 1 1 2 | 1 1 2 2 | 1 1 2 ----------------+----+--------+---------+------ x . demi( . . ) | 2 | 6 * * | 0 1 2 0 | 1 0 2 . x demi( . . ) | 2 | * 6 * | 0 1 0 2 | 0 1 2 . . sefa( s3s ) | 2 | * * 12 | 1 0 1 1 | 1 1 1 ----------------+----+--------+---------+------ . . s3s ♦ 3 | 0 0 3 | 4 * * * | 1 1 0 x x demi( . . ) | 4 | 2 2 0 | * 3 * * | 0 0 2 x . sefa( s3s ) | 4 | 2 0 2 | * * 6 * | 1 0 1 . x sefa( s3s ) | 4 | 0 2 2 | * * * 6 | 0 1 1 ----------------+----+--------+---------+------ x . s3s ♦ 6 | 3 0 6 | 2 0 3 0 | 2 * * . x s3s ♦ 6 | 0 3 6 | 2 0 0 3 | * 2 * x x sefa( s3s ) ♦ 8 | 4 4 4 | 0 2 2 2 | * * 3
xx xx3oo&#x → height = 1
(trip || trip)
o. o.3o. | 6 * ♦ 1 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
.o .o3.o | * 6 ♦ 0 0 1 1 2 | 0 0 1 2 2 1 | 0 2 1 1
------------+-----+-----------+-------------+--------
x. .. .. | 2 0 | 3 * * * * | 2 0 1 0 0 0 | 1 2 0 0
.. x. .. | 2 0 | * 6 * * * | 1 1 0 1 0 0 | 1 1 1 0
oo oo3oo&#x | 1 1 | * * 6 * * | 0 0 1 2 0 0 | 0 2 1 0
.x .. .. | 0 2 | * * * 3 * | 0 0 1 0 2 0 | 0 2 0 1
.. .x .. | 0 2 | * * * * 6 | 0 0 0 1 1 1 | 0 1 1 1
------------+-----+-----------+-------------+--------
x. x. .. | 4 0 | 2 2 0 0 0 | 3 * * * * * | 1 1 0 0
.. x.3o. | 3 0 | 0 3 0 0 0 | * 2 * * * * | 1 0 1 0
xx .. ..&#x | 2 2 | 1 0 2 1 0 | * * 3 * * * | 0 2 0 0
.. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * 6 * * | 0 1 1 0
.x .x .. | 0 4 | 0 0 0 2 2 | * * * * 3 * | 0 1 0 1
.. .x3.o | 0 3 | 0 0 0 0 3 | * * * * * 2 | 0 0 1 1
------------+-----+-----------+-------------+--------
x. x.3o. ♦ 6 0 | 3 6 0 0 0 | 3 2 0 0 0 0 | 1 * * *
xx xx ..&#x ♦ 4 4 | 2 2 4 2 2 | 1 0 2 2 1 0 | * 3 * *
.. xx3oo&#x ♦ 3 3 | 0 3 3 0 3 | 0 1 0 3 0 1 | * * 2 *
.x .x3.o ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 3 2 | * * * 1
ox xx4oo&#x → height = sqrt(3)/2 = 0.866025
({4} || cube)
o. o.4o. | 4 * ♦ 2 2 0 0 | 1 1 4 0 0 | 2 2 0
.o .o4.o | * 8 ♦ 0 1 1 2 | 0 1 2 2 1 | 2 1 1
------------+-----+---------+-----------+------
.. x. .. | 2 0 | 4 * * * | 1 0 2 0 0 | 1 2 0
oo oo4oo&#x | 1 1 | * 8 * * | 0 1 2 0 0 | 2 1 0
.x .. .. | 0 2 | * * 4 * | 0 1 0 2 0 | 2 0 1
.. .x .. | 0 2 | * * * 8 | 0 0 1 1 1 | 1 1 1
------------+-----+---------+-----------+------
.. x.4o. | 4 0 | 4 0 0 0 | 1 * * * * | 0 2 0
ox .. ..&#x | 1 2 | 0 2 1 0 | * 4 * * * | 2 0 0
.. xx ..&#x | 2 2 | 1 2 0 1 | * * 8 * * | 1 1 0
.x .x .. | 0 4 | 0 0 2 2 | * * * 4 * | 1 0 1
.. .x4.o | 0 4 | 0 0 0 4 | * * * * 2 | 0 1 1
------------+-----+---------+-----------+------
ox xx ..&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 1 0 | 4 * *
.. xx4oo&#x ♦ 4 4 | 4 4 0 4 | 1 0 4 0 1 | * 2 *
.x .x4.o ♦ 0 8 | 0 0 4 8 | 0 0 0 4 2 | * * 1
ox xx xx&#x → height = sqrt(3)/2 = 0.866025
({4} || cube)
o. o. o. | 4 * ♦ 1 1 2 0 0 0 | 1 1 2 2 0 0 0 | 1 1 2 0
.o .o .o | * 8 ♦ 0 0 1 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1
------------+-----+-------------+---------------+--------
.. x. .. | 2 0 | 2 * * * * * | 1 0 2 0 0 0 0 | 1 0 2 0
.. .. x. | 2 0 | * 2 * * * * | 1 0 0 2 0 0 0 | 0 1 2 0
oo oo oo&#x | 1 1 | * * 8 * * * | 0 1 1 1 0 0 0 | 1 1 1 0
.x .. .. | 0 2 | * * * 4 * * | 0 1 0 0 1 1 0 | 1 1 0 1
.. .x .. | 0 2 | * * * * 4 * | 0 0 1 0 1 0 1 | 1 0 1 1
.. .. .x | 0 2 | * * * * * 4 | 0 0 0 1 0 1 1 | 0 1 1 1
------------+-----+-------------+---------------+--------
.. x. x. | 4 0 | 2 2 0 0 0 0 | 1 * * * * * * | 0 0 2 0
ox .. ..&#x | 1 2 | 0 0 2 1 0 0 | * 4 * * * * * | 1 1 0 0
.. xx ..&#x | 2 2 | 1 0 2 0 1 0 | * * 4 * * * * | 1 0 1 0
.. .. xx&#x | 2 2 | 0 1 2 0 0 1 | * * * 4 * * * | 0 1 1 0
.x .x .. | 0 4 | 0 0 0 2 2 0 | * * * * 2 * * | 1 0 0 1
.x .. .x | 0 4 | 0 0 0 2 0 2 | * * * * * 2 * | 0 1 0 1
.. .x .x | 0 4 | 0 0 0 0 2 2 | * * * * * * 2 | 0 0 1 1
------------+-----+-------------+---------------+--------
ox xx ..&#x ♦ 2 4 | 1 0 4 2 2 0 | 0 2 2 0 1 0 0 | 2 * * *
ox .. xx&#x ♦ 2 4 | 1 0 4 2 0 2 | 0 2 0 2 0 1 0 | * 2 * *
.. xx xx&#x ♦ 4 4 | 2 2 4 0 2 2 | 1 0 2 2 0 0 1 | * * 2 *
.x .x .x ♦ 0 8 | 0 0 0 4 4 4 | 0 0 0 0 2 2 2 | * * * 1
xxx3ooo oqo&#xt → both heights = 1/sqrt(2) = 0.707107 ({3} || pseudo q x3o || {3}) o..3o.. o.. | 3 * * | 2 2 0 0 0 | 1 4 1 0 0 0 | 2 2 0 .o.3.o. .o. | * 6 * | 0 1 2 1 0 | 0 2 1 1 2 0 | 1 2 1 ..o3..o ..o | * * 3 | 0 0 0 2 2 | 0 0 1 0 4 1 | 0 2 2 ----------------+-------+-----------+-------------+------ x.. ... ... | 2 0 0 | 3 * * * * | 1 2 0 0 0 0 | 2 1 0 oo.3oo. oo.&#x | 1 1 0 | * 6 * * * | 0 2 1 0 0 0 | 1 2 0 .x. ... ... | 0 2 0 | * * 6 * * | 0 1 0 1 1 0 | 1 1 1 .oo3.oo .oo&#x | 0 1 1 | * * * 6 * | 0 0 1 0 2 0 | 0 2 1 ..x ... ... | 0 0 2 | * * * * 3 | 0 0 0 0 2 1 | 0 1 2 ----------------+-------+-----------+-------------+------ x..3o.. ... | 3 0 0 | 3 0 0 0 0 | 1 * * * * * | 2 0 0 xx. ... ...&#x | 2 2 0 | 1 2 1 0 0 | * 6 * * * * | 1 1 0 ... ... oqo&#xt | 1 2 1 | 0 2 0 2 0 | * * 3 * * * | 0 2 0 .x.3.o. ... | 0 3 0 | 0 0 3 0 0 | * * * 2 * * | 1 0 1 .xx ... ...&#x | 0 2 2 | 0 0 1 2 1 | * * * * 6 * | 0 1 1 ..x3..o ... | 0 0 3 | 0 0 0 0 3 | * * * * * 1 | 0 0 2 ----------------+-------+-----------+-------------+------ xx.3oo. ...&#x ♦ 3 3 0 | 3 3 3 0 0 | 1 3 0 1 0 0 | 2 * * xxx ... oqo&#xt ♦ 2 4 2 | 1 4 2 4 1 | 0 2 2 0 2 0 | * 3 * .xx3.oo ...&#x ♦ 0 3 3 | 0 0 3 3 3 | 0 0 0 1 3 1 | * * 2
or o..3o.. o.. & | 6 * | 2 2 0 | 1 4 1 0 | 2 2 .o.3.o. .o. | * 6 | 0 2 2 | 0 4 1 1 | 2 2 ------------------+-----+--------+----------+---- x.. ... ... & | 2 0 | 6 * * | 1 2 0 0 | 2 1 oo.3oo. oo.&#x & | 1 1 | * 12 * | 0 2 1 0 | 1 2 .x. ... ... | 0 2 | * * 6 | 0 2 0 1 | 2 1 ------------------+-----+--------+----------+---- x..3o.. ... & | 3 0 | 3 0 0 | 2 * * * | 2 0 xx. ... ...&#x & | 2 2 | 1 2 1 | * 12 * * | 1 1 ... ... oqo&#xt | 2 2 | 0 4 0 | * * 3 * | 0 2 .x.3.o. ... | 0 3 | 0 0 3 | * * * 2 | 2 0 ------------------+-----+--------+----------+---- xx.3oo. ...&#x & ♦ 3 3 | 3 3 3 | 1 3 0 1 | 4 * xxx ... oqo&#xt ♦ 4 4 | 2 8 2 | 0 4 2 0 | * 3
xxx xxx&#x → all lacing heights = 1 o.. o.. | 4 * * | 1 1 1 1 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0 .o. .o. | * 4 * | 0 0 1 0 1 1 1 0 0 | 0 1 1 0 0 1 1 1 1 0 | 1 0 1 1 1 ..o ..o | * * 4 | 0 0 0 0 0 0 1 1 1 | 0 0 0 1 1 1 0 1 1 1 | 0 1 1 1 1 -----------+-------+-------------------+---------------------+---------- x.. ... | 2 0 0 | 2 * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 | 1 1 1 0 0 ... x.. | 2 0 0 | * 2 * * * * * * * | 1 0 1 0 1 0 0 0 0 0 | 1 1 0 1 0 oo. oo.&#x | 1 1 0 | * * 4 * * * * * * | 0 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0 o.o o.o&#x | 1 0 0 | * * * 4 * * * * * | 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0 .x. ... | 0 2 0 | * * * * 2 * * * * | 0 1 0 0 0 0 1 1 0 0 | 1 0 1 0 1 ... .x. | 0 2 0 | * * * * * 2 * * * | 0 0 1 0 0 0 1 0 1 0 | 1 0 0 1 1 .oo .oo&#x | 0 1 1 | * * * * * * 4 * * | 0 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1 ..x ... | 0 0 2 | * * * * * * * 2 * | 0 0 0 1 0 0 0 1 0 1 | 0 1 1 0 1 ... ..x | 0 0 2 | * * * * * * * * 2 | 0 0 0 0 1 0 0 0 1 1 | 0 1 0 1 1 -----------+-------+-------------------+---------------------+---------- x.. x.. | 4 0 0 | 2 2 0 0 0 0 0 0 0 | 1 * * * * * * * * * | 1 1 0 0 0 xx. ...&#x | 2 2 0 | 1 0 2 0 1 0 0 0 0 | * 2 * * * * * * * * | 1 0 1 0 0 ... xx.&#x | 2 2 0 | 0 1 2 0 0 1 0 0 0 | * * 2 * * * * * * * | 1 0 0 1 0 x.x ...&#x | 2 0 2 | 1 0 0 2 0 0 0 1 0 | * * * 2 * * * * * * | 0 1 1 0 0 ... x.x&#x | 2 0 2 | 0 1 0 2 0 0 0 0 1 | * * * * 2 * * * * * | 0 1 0 1 0 ooo ooo&#x | 1 1 1 | 0 0 1 1 0 0 1 0 0 | * * * * * 4 * * * * | 0 0 1 1 0 .x. .x. | 0 4 0 | 0 0 0 0 2 2 0 0 0 | * * * * * * 1 * * * | 1 0 0 0 1 .xx ...&#x | 0 2 2 | 0 0 0 0 1 0 2 1 0 | * * * * * * * 2 * * | 0 0 1 0 1 ... .xx&#x | 0 2 2 | 0 0 0 0 0 1 2 0 1 | * * * * * * * * 2 * | 0 0 0 1 1 ..x ..x | 0 0 4 | 0 0 0 0 0 0 0 2 2 | * * * * * * * * * 1 | 0 1 0 0 1 -----------+-------+-------------------+---------------------+---------- xx. xx.&#x ♦ 4 4 0 | 2 2 4 0 2 2 0 0 0 | 1 2 2 0 0 0 1 0 0 0 | 1 * * * * x.x x.x&#x ♦ 4 0 4 | 2 2 0 4 0 0 0 2 2 | 1 0 0 2 2 0 0 0 0 1 | * 1 * * * xxx ...&#x ♦ 2 2 2 | 1 0 2 2 1 0 2 1 0 | 0 1 0 1 0 2 0 1 0 0 | * * 2 * * ... xxx&#x ♦ 2 2 2 | 0 1 2 2 0 1 2 0 1 | 0 0 1 0 1 2 0 0 1 0 | * * * 2 * .xx .xx&#x ♦ 0 4 4 | 0 0 0 0 2 2 4 2 2 | 0 0 0 0 0 0 1 2 2 1 | * * * * 1
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