Acronym tricupe, K-4.45
Name triangular-cupola prism,
triangular prism atop hexagonal prism
Segmentochoron display  
Circumradius sqrt(5)/2 = 1.118034
Lace city
in approx. ASCII-art
x3o  x3x	-- tricu
        
        
x3o  x3x	-- tricu

 |    +- hip
 +------ trip
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {4} between cube and trip:   arccos(-1/sqrt(3)) = 125.264390°
  • at {4} between cube and tricu:   90°
  • at {6} between hip and tricu:   90°
  • at {3} between tricu and trip:   90°
  • at {4} between hip and trip:   arccos(1/3) = 70.528779°
  • at {4} between cube and hip:   arccos(1/sqrt(3)) = 54.735610°
Confer
more general:
n/d-cupe  
uniform relative:
cope  
related segmentochora:
tobcupe  
general polytopal classes:
segmentochora  

Incidence matrix according to Dynkin symbol

xx3ox xx&#x   → height = sqrt(2/3) = 0.816497
(trip || hip)

o.3o. o.    | 6  *  2 1  2 0 0 0 | 1 2 2 1 2 0 0 0 | 1 1 2 1 0
.o3.o .o    | * 12 | 0 0  1 1 1 1 | 0 0 1 1 1 1 1 1 | 0 1 1 1 1
------------+------+--------------+-----------------+----------
x. .. ..    | 2  0 | 6 *  * * * * | 1 1 1 0 0 0 0 0 | 1 1 1 0 0
.. .. x.    | 2  0 | * 3  * * * * | 0 2 0 0 2 0 0 0 | 1 0 2 1 0
oo3oo oo&#x | 1  1 | * * 12 * * * | 0 0 1 1 1 0 0 0 | 0 1 1 1 0
.x .. ..    | 0  2 | * *  * 6 * * | 0 0 1 0 0 1 1 0 | 0 1 1 0 1
.. .x ..    | 0  2 | * *  * * 6 * | 0 0 0 1 0 1 0 1 | 0 1 0 1 1
.. .. .x    | 0  2 | * *  * * * 6 | 0 0 0 0 1 0 1 1 | 0 0 1 1 1
------------+------+--------------+-----------------+----------
x.3o. ..    | 3  0 | 3 0  0 0 0 0 | 2 * * * * * * * | 1 1 0 0 0
x. .. x.    | 4  0 | 2 2  0 0 0 0 | * 3 * * * * * * | 1 0 1 0 0
xx .. ..&#x | 2  2 | 1 0  2 1 0 0 | * * 6 * * * * * | 0 1 1 0 0
.. ox ..&#x | 1  2 | 0 0  2 0 1 0 | * * * 6 * * * * | 0 1 0 1 0
.. .. xx&#x | 2  2 | 0 1  2 0 0 1 | * * * * 6 * * * | 0 0 1 1 0
.x3.x ..    | 0  6 | 0 0  0 3 3 0 | * * * * * 2 * * | 0 1 0 0 1
.x .. .x    | 0  4 | 0 0  0 2 0 2 | * * * * * * 3 * | 0 0 1 0 1
.. .x .x    | 0  4 | 0 0  0 0 2 2 | * * * * * * * 3 | 0 0 0 1 1
------------+------+--------------+-----------------+----------
x.3o. x.     6  0 | 6 3  0 0 0 0 | 2 3 0 0 0 0 0 0 | 1 * * * *
xx3ox ..&#x  3  6 | 3 0  6 3 3 0 | 1 0 3 3 0 1 0 0 | * 2 * * *
xx .. xx&#x  4  4 | 2 2  4 2 0 2 | 0 1 2 0 2 0 1 0 | * * 3 * *
.. ox xx&#x  2  4 | 0 1  4 0 2 2 | 0 0 0 2 2 0 0 1 | * * * 3 *
.x3.x .x     0 12 | 0 0  0 6 6 6 | 0 0 0 0 0 2 3 3 | * * * * 1

xx3ox&#x || xx3ox&#x   → height = 1
(tricu || tricu)

o.3o.    || .. ..    | 3 * * *  2 2 1 0 0 0 0 0 0 0 | 1 2 1 2 2 0 0 0 0 0 0 0 | 1 1 2 1 0 0
.o3.o    || .. ..    | * 6 * * | 0 1 0 1 1 1 0 0 0 0 | 0 1 1 0 1 1 1 1 0 0 0 0 | 1 0 1 1 1 0
.. ..    || o.3o.    | * * 3 *  0 0 1 0 0 0 2 2 0 0 | 0 0 0 2 2 0 0 0 1 2 1 0 | 0 1 2 1 0 1
.. ..    || .o3.o    | * * * 6 | 0 0 0 0 0 1 0 1 1 1 | 0 0 0 0 1 0 1 1 0 1 1 1 | 0 0 1 1 1 1
---------------------+---------+---------------------+-------------------------+------------
x. ..    || .. ..    | 2 0 0 0 | 3 * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
oo3oo&#x || .. ..    | 1 1 0 0 | * 6 * * * * * * * * | 0 1 1 0 1 0 0 0 0 0 0 0 | 1 0 1 1 0 0
o.3o.    || o.3o.    | 1 0 1 0 | * * 3 * * * * * * * | 0 0 0 2 2 0 0 0 0 0 0 0 | 0 1 2 1 0 0
.x ..    || .. ..    | 0 2 0 0 | * * * 3 * * * * * * | 0 1 0 0 0 1 1 0 0 0 0 0 | 1 0 1 0 1 0
.. .x    || .. ..    | 0 2 0 0 | * * * * 3 * * * * * | 0 0 1 0 0 1 0 1 0 0 0 0 | 1 0 0 1 1 0
.o3.o    || .o3.o    | 0 1 0 1 | * * * * * 6 * * * * | 0 0 0 0 1 0 1 1 0 0 0 0 | 0 0 1 1 1 0
.. ..    || x. ..    | 0 0 2 0 | * * * * * * 3 * * * | 0 0 0 1 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
.. ..    || oo3oo&#x | 0 0 1 1 | * * * * * * * 6 * * | 0 0 0 0 1 0 0 0 0 1 1 0 | 0 0 1 1 0 1
.. ..    || .x ..    | 0 0 0 2 | * * * * * * * * 3 * | 0 0 0 0 0 0 1 0 0 1 0 1 | 0 0 1 0 1 1
.. ..    || .. .x    | 0 0 0 2 | * * * * * * * * * 3 | 0 0 0 0 0 0 0 1 0 0 1 1 | 0 0 0 1 1 1
---------------------+---------+---------------------+-------------------------+------------
x.3o.    || .. ..    | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * | 1 1 0 0 0 0
xx ..&#x || .. ..    | 2 2 0 0 | 1 2 0 1 0 0 0 0 0 0 | * 3 * * * * * * * * * * | 1 0 1 0 0 0
.. ox&#x || .. ..    | 1 2 0 0 | 0 2 0 0 1 0 0 0 0 0 | * * 3 * * * * * * * * * | 1 0 0 1 0 0
x. ..    || x. ..    | 2 0 2 0 | 1 0 2 0 0 0 1 0 0 0 | * * * 3 * * * * * * * * | 0 1 1 0 0 0
oo3oo&#x || oo3oo&#x | 1 1 1 1 | 0 1 1 0 0 1 0 1 0 0 | * * * * 6 * * * * * * * | 0 0 1 1 0 0
.x3.x    || .. ..    | 0 6 0 0 | 0 0 0 3 3 0 0 0 0 0 | * * * * * 1 * * * * * * | 1 0 0 0 1 0
.x ..    || .x ..    | 0 2 0 2 | 0 0 0 1 0 2 0 0 1 0 | * * * * * * 3 * * * * * | 0 0 1 0 1 0
.. .x    || .. .x    | 0 2 0 2 | 0 0 0 0 1 2 0 0 0 1 | * * * * * * * 3 * * * * | 0 0 0 1 1 0
.. ..    || x.3o.    | 0 0 3 0 | 0 0 0 0 0 0 3 0 0 0 | * * * * * * * * 1 * * * | 0 1 0 0 0 1
.. ..    || xx ..&#x | 0 0 2 2 | 0 0 0 0 0 0 1 2 1 0 | * * * * * * * * * 3 * * | 0 0 1 0 0 1
.. ..    || .. ox&#x | 0 0 1 2 | 0 0 0 0 0 0 0 2 0 1 | * * * * * * * * * * 3 * | 0 0 0 1 0 1
.. ..    || .x3.x    | 0 0 0 6 | 0 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * 1 | 0 0 0 0 1 1
---------------------+---------+---------------------+-------------------------+------------
xx3ox&#x || .. ..     3 6 0 0 | 3 6 0 3 3 0 0 0 0 0 | 1 3 3 0 0 1 0 0 0 0 0 0 | 1 * * * * *
x.3o.    || x.3o.     3 0 3 0 | 3 0 3 0 0 0 3 0 0 0 | 1 0 0 3 0 0 0 0 1 0 0 0 | * 1 * * * *
xx ..&#x || xx ..&#x  2 2 2 2 | 1 2 2 1 0 2 1 2 1 0 | 0 1 0 1 2 0 1 0 0 1 0 0 | * * 3 * * *
.. ox&#x || .. ox&#x  1 2 1 2 | 0 2 1 0 1 2 0 2 0 1 | 0 0 1 0 2 0 0 1 0 0 1 0 | * * * 3 * *
.x3.x    || .x3.x     0 6 0 6 | 0 0 0 3 3 6 0 0 3 3 | 0 0 0 0 0 1 3 3 0 0 0 1 | * * * * 1 *
.. ..    || xx3ox&#x  0 0 3 6 | 0 0 0 0 0 0 3 6 3 3 | 0 0 0 0 0 0 0 0 1 3 3 1 | * * * * * 1

© 2004-2019
top of page