Acronym rite (alt.: ikaidbicu)
Name rectified ite,
ikaid bicupola
Circumradius ...
Lace city
in approx. ASCII-art 
    x5o    
           
           
o5o     o5o
    o5f    
           
           
x5o     x5o
           
           
    x5x    
           
           
o5x     o5x
           
           
    f5o    
o5o     o5o
           
           
    o5x    

        x3o   o3f f3o   o3x        
                                   		F=ff=x+f=2x+v
o3x   x3f F3o   f3f   o3F f3x   x3o
                                   
        x3o   o3f f3o   o3x
Dihedral angles
  • at {3} between oct and oct (lacing):   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between ike and oct:   arccos(-sqrt[7+3 sqrt(5)]/4) = 157.761244°
  • at {3} between oct and peppy:   arccos(-sqrt[7+3 sqrt(5)]/4) = 157.761244°
  • at {5} between peppy and peppy:   72°
  • at {3} between oct and oct (equatorial):   arccos[(3 sqrt(5)-1)/8] = 44.477512°
Face vector 54, 240, 252, 66
Confer
uniform relative:
rox  
related segmentochora:
ikaid  
ambification pre-image:
ite  
general polytopal classes:
bistratic lace towers  

Rectification wrt. a non-regular polytope is meant to be the singular instance of truncations on all vertices at such a depth that the hyperplane intersections on the former edges will coincide (provided such a choice exists). Within the specific case of ite as a pre-image these intersection points might differ on its 3 edge types. However, both this polychoron as well as the pre-image here is a bistratic blend of segmentochora, which in turn are diminishings of rectified and regular polychora respectively. From this embedding it well becomes clear that rectification here would apply none the less.

Its construction as segmentochoric bicupola moreover makes clear that it also happens to be a CRF.


Incidence matrix according to Dynkin symbol

rect( ouo3ooo5ooo&#ut = ite ) =
xox3oxo5ooo&#xt   → both heights = [sqrt(5)-1]/4 = 0.309017
(ike || pseudo id || ike)

o..3o..5o..    | 12  *  * ♦  5  5  0  0  0 |  5  5  5  0  0  0  0  0 | 1  5  1  0  0 0
.o.3.o.5.o.    |  * 30  * |  0  2  4  2  0 |  0  1  4  2  2  1  4  0 | 0  2  2  2  2 0
..o3..o5..o    |  *  * 12 ♦  0  0  0  5  5 |  0  0  0  0  0  5  5  5 | 0  0  0  5  1 1
---------------+----------+----------------+-------------------------+----------------
x.. ... ...    |  2  0  0 | 30  *  *  *  * |  2  1  0  0  0  0  0  0 | 1  2  0  0  0 0
oo.3oo.5oo.&#x |  1  1  0 |  * 60  *  *  * |  0  1  2  0  0  0  0  0 | 0  2  1  0  0 0
... .x. ...    |  0  2  0 |  *  * 60  *  * |  0  0  1  1  1  0  1  0 | 0  1  1  1  1 0
.oo3.oo5.oo&#x |  0  1  1 |  *  *  * 60  * |  0  0  0  0  0  1  2  0 | 0  0  0  2  1 0
..x ... ...    |  0  0  2 |  *  *  *  * 30 |  0  0  0  0  0  1  0  2 | 0  0  0  2  0 1
---------------+----------+----------------+-------------------------+----------------
x..3o.. ...    |  3  0  0 |  3  0  0  0  0 | 20  *  *  *  *  *  *  * | 1  1  0  0  0 0
xo. ... ...&#x |  2  1  0 |  1  2  0  0  0 |  * 30  *  *  *  *  *  * | 0  2  0  0  0 0
... ox. ...&#x |  1  2  0 |  0  2  1  0  0 |  *  * 60  *  *  *  *  * | 0  1  1  0  0 0
.o.3.x. ...    |  0  3  0 |  0  0  3  0  0 |  *  *  * 20  *  *  *  * | 0  1  0  1  0 0
... .x.5.o.    |  0  5  0 |  0  0  5  0  0 |  *  *  *  * 12  *  *  * | 0  0  1  0  1 0
.ox ... ...&#x |  0  1  2 |  0  0  0  2  1 |  *  *  *  *  * 30  *  * | 0  0  0  2  0 0
... .xo ...&#x |  0  2  1 |  0  0  1  2  0 |  *  *  *  *  *  * 60  * | 0  0  0  1  1 0
..x3..o ...    |  0  0  3 |  0  0  0  0  3 |  *  *  *  *  *  *  * 20 | 0  0  0  1  0 1
---------------+----------+----------------+-------------------------+----------------
x..3o..5o..    ♦ 12  0  0 | 30  0  0  0  0 | 20  0  0  0  0  0  0  0 | 1  *  *  *  * *
xo.3ox. ...&#x ♦  3  3  0 |  3  6  3  0  0 |  1  3  3  1  0  0  0  0 | * 20  *  *  * *
... ox.5oo.&#x ♦  1  5  0 |  0  5  5  0  0 |  0  0  5  0  1  0  0  0 | *  * 12  *  * *
.ox3.xo ...&#x ♦  0  3  3 |  0  0  3  6  3 |  0  0  0  1  0  3  3  1 | *  *  * 20  * *
... .xo5.oo&#x ♦  0  5  1 |  0  0  5  5  0 |  0  0  0  0  1  0  5  0 | *  *  *  * 12 *
..x3..o5..o    ♦  0  0 12 |  0  0  0  0 30 |  0  0  0  0  0  0  0 20 | *  *  *  *  * 1

or
o..3o..5o..    & | 24  * ♦  5   5  0 |  5  5   5  0  0 | 1  5  1
.o.3.o.5.o.      |  * 30 |  0   4  4 |  0  2   8  2  2 | 0  4  4
-----------------+-------+-----------+-----------------+--------
x.. ... ...    & |  2  0 | 60   *  * |  2  1   0  0  0 | 1  2  0
oo.3oo.5oo.&#x & |  1  1 |  * 120  * |  0  1   2  0  0 | 0  2  1
... .x. ...      |  0  2 |  *   * 60 |  0  0   2  1  1 | 0  2  2
-----------------+-------+-----------+-----------------+--------
x..3o.. ...    & |  3  0 |  3   0  0 | 40  *   *  *  * | 1  1  0
xo. ... ...&#x & |  2  1 |  1   2  0 |  * 60   *  *  * | 0  2  0
... ox. ...&#x & |  1  2 |  0   2  1 |  *  * 120  *  * | 0  1  1
.o.3.x. ...      |  0  3 |  0   0  3 |  *  *   * 20  * | 0  2  0
... .x.5.o.      |  0  5 |  0   0  5 |  *  *   *  * 12 | 0  0  2
-----------------+-------+-----------+-----------------+--------
x..3o..5o..    & ♦ 12  0 | 30   0  0 | 20  0   0  0  0 | 2  *  *
xo.3ox. ...&#x & ♦  3  3 |  3   6  3 |  1  3   3  1  0 | * 40  *
... ox.5oo.&#x & ♦  1  5 |  0   5  5 |  0  0   5  0  1 | *  * 24

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