Acronym thiddip, K-4.47
Name triangle - hexagon duoprism,
hexagon - hip wedge
 
 
 ©
Circumradius sqrt(4/3) = 1.154701
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {3} between trip and trip:   120°
  • at {4} between hip and trip:   90°
  • at {6} between hip and hip:   60°
Confer
general duoprisms:
n,m-dip   2n,m-dip   3,n-dip   6,n-dip  
general polytopal classes:
segmentochora   bistratic lace towers  
External
links
hedrondude   wikipedia

Incidence matrix according to Dynkin symbol

x3o x6o

. . . . | 18 |  2  2 | 1  4 1 | 2 2
--------+----+-------+--------+----
x . . . |  2 | 18  * | 1  2 0 | 2 1
. . x . |  2 |  * 18 | 0  2 1 | 1 2
--------+----+-------+--------+----
x3o . . |  3 |  3  0 | 6  * * | 2 0
x . x . |  4 |  2  2 | * 18 * | 1 1
. . x6o |  6 |  0  6 | *  * 3 | 0 2
--------+----+-------+--------+----
x3o x .   6 |  6  3 | 2  3 0 | 6 *
x . x6o  12 |  6 12 | 0  6 2 | * 3

x3o x6/5o

. . .   . | 18 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x . .   . |  2 | 18  * | 1  2 0 | 2 1
. . x   . |  2 |  * 18 | 0  2 1 | 1 2
----------+----+-------+--------+----
x3o .   . |  3 |  3  0 | 6  * * | 2 0
x . x   . |  4 |  2  2 | * 18 * | 1 1
. . x6/5o |  6 |  0  6 | *  * 3 | 0 2
----------+----+-------+--------+----
x3o x   .   6 |  6  3 | 2  3 0 | 6 *
x . x6/5o  12 |  6 12 | 0  6 2 | * 3

x3/2o x6o

.   . . . | 18 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x   . . . |  2 | 18  * | 1  2 0 | 2 1
.   . x . |  2 |  * 18 | 0  2 1 | 1 2
----------+----+-------+--------+----
x3/2o . . |  3 |  3  0 | 6  * * | 2 0
x   . x . |  4 |  2  2 | * 18 * | 1 1
.   . x6o |  6 |  0  6 | *  * 3 | 0 2
----------+----+-------+--------+----
x3/2o x .   6 |  6  3 | 2  3 0 | 6 *
x   . x6o  12 |  6 12 | 0  6 2 | * 3

x3/2o x6/5o

.   . .   . | 18 |  2  2 | 1  4 1 | 2 2
------------+----+-------+--------+----
x   . .   . |  2 | 18  * | 1  2 0 | 2 1
.   . x   . |  2 |  * 18 | 0  2 1 | 1 2
------------+----+-------+--------+----
x3/2o .   . |  3 |  3  0 | 6  * * | 2 0
x   . x   . |  4 |  2  2 | * 18 * | 1 1
.   . x6/5o |  6 |  0  6 | *  * 3 | 0 2
------------+----+-------+--------+----
x3/2o x   .   6 |  6  3 | 2  3 0 | 6 *
x   . x6/5o  12 |  6 12 | 0  6 2 | * 3

x3x x3o

. . . . | 18 | 1 1  2 | 1 2 2 1 | 2 1 1
--------+----+--------+---------+------
x . . . |  2 | 9 *  * | 1 2 0 0 | 2 1 0
. x . . |  2 | * 9  * | 1 0 2 0 | 2 0 1
. . x . |  2 | * * 18 | 0 1 1 1 | 1 1 1
--------+----+--------+---------+------
x3x . . |  6 | 3 3  0 | 3 * * * | 2 0 0
x . x . |  4 | 2 0  2 | * 9 * * | 1 1 0
. x x . |  4 | 0 2  2 | * * 9 * | 1 0 1
. . x3o |  3 | 0 0  3 | * * * 6 | 0 1 1
--------+----+--------+---------+------
x3x x .  12 | 6 6  6 | 2 3 3 0 | 3 * *
x . x3o   6 | 3 0  6 | 0 3 0 2 | * 3 *
. x x3o   6 | 0 3  6 | 0 0 3 2 | * * 3

snubbed forms: s3s2x3o

x3x x3/2o

. . .   . | 18 | 1 1  2 | 1 2 2 1 | 2 1 1
----------+----+--------+---------+------
x . .   . |  2 | 9 *  * | 1 2 0 0 | 2 1 0
. x .   . |  2 | * 9  * | 1 0 2 0 | 2 0 1
. . x   . |  2 | * * 18 | 0 1 1 1 | 1 1 1
----------+----+--------+---------+------
x3x .   . |  6 | 3 3  0 | 3 * * * | 2 0 0
x . x   . |  4 | 2 0  2 | * 9 * * | 1 1 0
. x x   . |  4 | 0 2  2 | * * 9 * | 1 0 1
. . x3/2o |  3 | 0 0  3 | * * * 6 | 0 1 1
----------+----+--------+---------+------
x3x x   .  12 | 6 6  6 | 2 3 3 0 | 3 * *
x . x3/2o   6 | 3 0  6 | 0 3 0 2 | * 3 *
. x x3/2o   6 | 0 3  6 | 0 0 3 2 | * * 3

s3s x3x

demi( . . ) . . | 18 | 1 1  2 | 1 1 2 2 | 1 1 2
----------------+----+--------+---------+------
demi( . . ) x . |  2 | 9 *  * | 1 0 2 0 | 1 0 2
demi( . . ) . x |  2 | * 9  * | 1 0 0 2 | 0 1 2
sefa( s3s ) . . |  2 | * * 18 | 0 1 1 1 | 1 1 1
----------------+----+--------+---------+------
demi( . . ) x3x |  6 | 3 3  0 | 3 * * * | 0 0 2
      s3s   . . |  3 | 0 0  3 | * 6 * * | 1 1 0
sefa( s3s ) x . |  4 | 2 0  2 | * * 9 * | 1 0 1
sefa( s3s ) . x |  4 | 0 2  2 | * * * 9 | 0 1 1
----------------+----+--------+---------+------
      s3s   x .   6 | 3 0  6 | 0 2 3 0 | 3 * *
      s3s   . x   6 | 0 3  6 | 0 2 0 3 | * 3 *
sefa( s3s ) x3x  12 | 6 6  6 | 2 0 3 3 | * * 3

s3s2x3x

demi( . . . . ) | 18 | 1 1  2 | 1 1 2 2 | 1 1 2
----------------+----+--------+---------+------
demi( . . x . ) |  2 | 9 *  * | 1 0 2 0 | 1 0 2
demi( . . . x ) |  2 | * 9  * | 1 0 0 2 | 0 1 2
sefa( s3s . . ) |  2 | * * 18 | 0 1 1 1 | 1 1 1
----------------+----+--------+---------+------
demi( . . x3x ) |  6 | 3 3  0 | 3 * * * | 0 0 2
      s3s . .   |  3 | 0 0  3 | * 6 * * | 1 1 0
sefa( s3s2x . ) |  4 | 2 0  2 | * * 9 * | 1 0 1
sefa( s3s 2 x ) |  4 | 0 2  2 | * * * 9 | 0 1 1
----------------+----+--------+---------+------
      s3s2x .     6 | 3 0  6 | 0 2 3 0 | 3 * *
      s3s 2 x     6 | 0 3  6 | 0 2 0 3 | * 3 *
sefa( s3s2x3x )  12 | 6 6  6 | 2 0 3 3 | * * 3

starting figure: x3x x3x

ox xx3xx&#x   → height = sqrt(3)/2 = 0.866025
({6} || hip)

o. o.3o.    | 6  * | 1 1  2 0 0 0 | 1 1 2 2 0 0 0 | 1 1 2 0
.o .o3.o    | * 12 | 0 0  1 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1
------------+------+--------------+---------------+--------
.. x. ..    | 2  0 | 3 *  * * * * | 1 0 2 0 0 0 0 | 1 0 2 0
.. .. x.    | 2  0 | * 3  * * * * | 1 0 0 2 0 0 0 | 0 1 2 0
oo oo3oo&#x | 1  1 | * * 12 * * * | 0 1 1 1 0 0 0 | 1 1 1 0
.x .. ..    | 0  2 | * *  * 6 * * | 0 1 0 0 1 1 0 | 1 1 0 1
.. .x ..    | 0  2 | * *  * * 6 * | 0 0 1 0 1 0 1 | 1 0 1 1
.. .. .x    | 0  2 | * *  * * * 6 | 0 0 0 1 0 1 1 | 0 1 1 1
------------+------+--------------+---------------+--------
.. x.3x.    | 6  0 | 3 3  0 0 0 0 | 1 * * * * * * | 0 0 2 0
ox .. ..&#x | 1  2 | 0 0  2 1 0 0 | * 6 * * * * * | 1 1 0 0
.. xx ..&#x | 2  2 | 1 0  2 0 1 0 | * * 6 * * * * | 1 0 1 0
.. .. xx&#x | 2  2 | 0 1  2 0 0 1 | * * * 6 * * * | 0 1 1 0
.x .x ..    | 0  4 | 0 0  0 2 2 0 | * * * * 3 * * | 1 0 0 1
.x .. .x    | 0  4 | 0 0  0 2 0 2 | * * * * * 3 * | 0 1 0 1
.. .x3.x    | 0  6 | 0 0  0 0 3 3 | * * * * * * 2 | 0 0 1 1
------------+------+--------------+---------------+--------
ox xx ..&#x  2  4 | 1 0  4 2 2 0 | 0 2 2 0 1 0 0 | 3 * * *
ox .. xx&#x  2  4 | 0 1  4 2 0 2 | 0 2 0 2 0 1 0 | * 3 * *
.. xx3xx&#x  6  6 | 3 3  6 0 3 3 | 1 0 3 3 0 0 1 | * * 2 *
.x .x3.x     0 12 | 0 0  0 6 6 6 | 0 0 0 0 3 3 2 | * * * 1

xux xxx3ooo&#xt   → both heights = sqrt(3)/2 = 0.866025
(trip || pseudo (x,u)-trip || trip)

o.. o..3o..     | 6 * * | 1 2 1 0 0 0 0 | 2 1 2 1 0 0 0 0 | 1 1 2 0 0
.o. .o.3.o.     | * 6 * | 0 0 1 2 1 0 0 | 0 0 2 1 1 2 0 0 | 0 1 2 1 0
..o ..o3..o     | * * 6 | 0 0 0 0 1 1 2 | 0 0 0 1 0 2 2 1 | 0 0 2 1 1
----------------+-------+---------------+-----------------+----------
x.. ... ...     | 2 0 0 | 3 * * * * * * | 2 0 0 1 0 0 0 0 | 1 0 2 0 0
... x.. ...     | 2 0 0 | * 6 * * * * * | 1 1 1 0 0 0 0 0 | 1 1 1 0 0
oo. oo.3oo.&#x  | 1 1 0 | * * 6 * * * * | 0 0 2 1 0 0 0 0 | 0 1 2 0 0
... .x. ...     | 0 2 0 | * * * 6 * * * | 0 0 1 0 1 1 0 0 | 0 1 1 1 0
.oo .oo3.oo&#x  | 0 1 1 | * * * * 6 * * | 0 0 0 1 0 2 0 0 | 0 0 2 1 0
..x ... ...     | 0 0 2 | * * * * * 3 * | 0 0 0 1 0 0 2 0 | 0 0 2 0 1
... ..x ...     | 0 0 2 | * * * * * * 6 | 0 0 0 0 0 1 1 1 | 0 0 1 1 1
----------------+-------+---------------+-----------------+----------
x.. x.. ...     | 4 0 0 | 2 2 0 0 0 0 0 | 3 * * * * * * * | 1 0 1 0 0
... x..3o..     | 3 0 0 | 0 3 0 0 0 0 0 | * 2 * * * * * * | 1 1 0 0 0
... xx. ...&#x  | 2 2 0 | 0 1 2 1 0 0 0 | * * 6 * * * * * | 0 1 1 0 0
xux ... ...&#xt | 2 2 2 | 1 0 2 0 2 1 0 | * * * 3 * * * * | 0 0 2 0 0
... .x.3.o.     | 0 3 0 | 0 0 0 3 0 0 0 | * * * * 2 * * * | 0 1 0 1 0
... .xx ...&#x  | 0 2 2 | 0 0 0 1 2 0 1 | * * * * * 6 * * | 0 0 1 1 0
..x ..x ...     | 0 0 4 | 0 0 0 0 0 2 2 | * * * * * * 3 * | 0 0 1 0 1
... ..x3..o     | 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * * 2 | 0 0 0 1 1
----------------+-------+---------------+-----------------+----------
x.. x..3o..      6 0 0 | 3 6 0 0 0 0 0 | 3 2 0 0 0 0 0 0 | 1 * * * *
... xx.3oo.&#x   3 3 0 | 0 3 3 3 0 0 0 | 0 1 3 0 1 0 0 0 | * 2 * * *
xux xxx ...&#xt  4 4 4 | 2 2 4 2 4 2 2 | 1 0 2 2 0 2 1 0 | * * 3 * *
... .xx3.oo&#x   0 3 3 | 0 0 0 3 3 0 3 | 0 0 0 0 1 3 0 1 | * * * 2 *
..x ..x3..o      0 0 6 | 0 0 0 0 0 3 6 | 0 0 0 0 0 0 3 2 | * * * * 1
or
o.. o..3o..      & | 12 * | 1  2  1 0 | 2 1  2 1 0 | 1 1 2
.o. .o.3.o.        |  * 6 | 0  0  2 2 | 0 0  4 1 1 | 0 2 2
-------------------+------+-----------+------------+------
x.. ... ...      & |  2 0 | 6  *  * * | 2 0  0 1 0 | 1 0 2
... x.. ...      & |  2 0 | * 12  * * | 1 1  1 0 0 | 1 1 1
oo. oo.3oo.&#x   & |  1 1 | *  * 12 * | 0 0  2 1 0 | 0 1 2
... .x. ...        |  0 2 | *  *  * 6 | 0 0  2 0 1 | 0 2 1
-------------------+------+-----------+------------+------
x.. x.. ...      & |  4 0 | 2  2  0 0 | 6 *  * * * | 1 0 1
... x..3o..      & |  3 0 | 0  3  0 0 | * 4  * * * | 1 1 0
... xx. ...&#x   & |  2 2 | 0  1  2 1 | * * 12 * * | 0 1 1
xux ... ...&#xt    |  4 2 | 2  0  4 0 | * *  * 3 * | 0 0 2
... .x.3.o.        |  0 3 | 0  0  0 3 | * *  * * 2 | 0 2 0
-------------------+------+-----------+------------+------
x.. x..3o..      &   6 0 | 3  6  0 0 | 3 2  0 0 0 | 2 * *
... xx.3oo.&#x   &   3 3 | 0  3  3 3 | 0 1  3 0 1 | * 4 *
xux xxx ...&#xt      8 4 | 4  4  8 2 | 2 0  4 2 0 | * * 3

© 2004-2019
top of page