prico

Acronym prico

Name prismatorhombated icositetrachoron,
runcitruncated icositetrachoron

Circumradius sqrt[8+3 sqrt(2)] = 3.498949

©

Vertex layers

Layer	Symmetry	Subsymmetries
	`o3o4o3o`	`o3o4o .`	`o3o . o`	`o . o3o`	`. o4o3o`
1	`x3x4o3x`	`x3x4o .` toe first	`x3x . x` hip first	`x . o3x` trip first	`. x4o3x` sirco first
2		`x3x4x .`	`w3x . o`	`u . q3x`	`. u4o3x`
3a		`u3x4x .`	`x3u . w`	`x . Q3x`	`. x4q3x`
3b		`u3x4x .`	`x3u . w`	`D . o3w`	`. x4q3x`
4		`Q3x4o .`	`w3u . q`	`X . w3o`	`. u4o3w`
5a		`x3u4x .`	`u3x . Y`	`w . Y3o`	`. x4w3o`
5b		`x3u4x .`	`u3x . Y`	`Z . x3q`	`. x4w3o`
6a		`w3u4o .`	`x3X . w`	`x . Q3w`	`. x4o3Y`
6b		`w3u4o .`	`x3X . w`	`D . o3Y`	`. x4o3Y`
7a		`x3x4w .`	`w3D . o`	`U . x3o`	`. u4x3q`
7b		`x3x4w .`	`X3x . Q`	`U . x3o`	`. u4x3q`
8a		`w3x4q .`	`x3x . A`	`u . q3Y`	`. x4x3Q`
8b		`w3x4q .`	`x3x . A`	`u . q3Y`	`. D4x3o`
9a		`x3x4w .`	`x3Z . x`	`w . Y3q`	`. x4x3Q`
9b		`x3x4w .`	`u3w . Y`	`Z . x3q`	`. D4x3o`
10		`w3u4o .`	`x3w . A`	`x . o3A`	`. u4x3q`
11a		`x3u4x .`	`X3D . o`	`X . w3Q`	`. x4o3Y`
11b		`x3u4x .`	`Z3x . Q`	`X . w3Q`	`. x4o3Y`
12		`Q3x4o .`	`x3x . B`	`x . Y3w`	`. x4w3o`
13a		`u3x4x .`	`u3Z . x`	`w . A3o`	`. u4o3w`
13b		`u3x4x .`	`D3w . Y`	`C . x3o`	`. u4o3w`
14		`x3x4x .`	`Z3u . q`	`u . w3Y`	`. x4q3x`
15a		`x3x4o .` opposite toe	`D3X . w`	`U . x3Q`	`. u4o3x`
15b		`x3x4o .` opposite toe	`u3w . A`	`U . x3Q`	`. u4o3x`
16a			`x3U . o`	`x . x3A`	`. x4o3x` opposite sirco
16b			`Z3x . Y`	`x . A3x`	`. x4o3x` opposite sirco
17a			`u3x . B`	`Z . w3Q`
17b			`u3x . B`	`C . x3q`
18			`U3x . x`	`X . A3o`
19a			`Z3u . Y`	`D . w3Y`
19b			`X3x . A`	`D . w3Y`
20a			`u3Z . Y`	`U . o3Y`
20b			`x3X . A`	`U . o3Y`
21a			`x3U . x`	`Z . Y3q`
21b			`x3U . x`	`C . w3o`
22a			`x3u . B`	`x . x3A`
22b			`x3u . B`	`x . A3x`
23a			`U3x . o`	`Z . q3Y`
23b			`x3Z . Y`	`C . o3w`
24a			`X3D . w`	`U . Y3o`
24b			`w3u . A`	`U . Y3o`
25			`u3Z . q`	`D . Y3w`
26a			`Z3u . x`	`X . o3A`
26b			`w3D . Y`	`X . o3A`
27a			`x3x . B`	`Z . Q3w`
27b			`x3x . B`	`C . q3x`
28a			`D3X . o`	`x . x3A`
28b			`x3Z . Q`	`x . A3x`
29			`w3x . A`	`U . Q3x`
30a			`Z3x . x`	`u . Y3w`
30b			`w3u . Y`	`u . Y3w`
31a			`x3x . A`	`w . o3A`
31b			`x3x . A`	`C . o3x`
32a			`D3w . o`	`x . w3Y`
32b			`x3X . Q`	`x . w3Y`
33			`X3x . w`	`X . Q3w`
34			`x3u . Y`	`x . A3o`
35a			`u3w . q`	`w . q3Y`
35b			`u3w . q`	`Z . q3x`
36			`u3x . w`	`u . Y3q`
37			`x3w . o`	`U . o3x`
38a			`x3x . x` opposite hip	`x . w3Q`
38b			`x3x . x` opposite hip	`D . Y3o`
39a				`w . o3Y`
39b	`Z . q3x`
40	`X . o3w`
41a	`x . x3Q`
41b	`D . w3o`
42	`u . x3q`
43	`x . x3o` opposite trip

(D=3x, Q=2q, X=wq=x+w=2x+q, Y=x+2q=w+q, Z=3x+q=u+w, U=u+X=4x+q, A=Y+q=x+3q, B=A+x=2x+3q, C=5x+q)

Lace city
in approx. ASCII-art

©

              o4x   o4u   q4x   o4u   o4x              
                                                       
          x4x   x4u   w4x     w4x   x4u   x4x          
                                                       
                                                       
    x4x         x4D   w4u     w4u   x4D         x4x    
                                                       
o4x                 o4Z   q4X   o4Z                 o4x
    x4u   x4D         Y4x     Y4x         x4D   x4u    
                                                       
o4u           o4Z         Q4w         o4Z           o4u
    w4x   w4u   Y4x                 Y4x   w4u   w4x    
                                                       
q4x           q4X   Q4w         Q4w   q4X           q4x
                                                       
    w4x   w4u   Y4x                 Y4x   w4u   w4x    
o4u           o4Z         Q4w         o4Z           o4u
                                                       
    x4u   x4D         Y4x     Y4x         x4D   x4u    
o4x                 o4Z   q4X   o4Z                 o4x
                                                       
    x4x         x4D   w4u     w4u   x4D         x4x    
                                                       
                                                       
          x4x   x4u   w4x     w4x   x4u   x4x          
                                                       
              o4x   o4u   q4x   o4u   o4x

©

               x3x   u3x   x3u   x3x               
                                                   
         x3x x3w   u3w # x3X w3u   w3x x3x         
                      (X3x)                        
                                                   
      u3x u3w   D3w Z3x     x3Z w3D   w3u x3u      
                                                   
        X3x   Z3x                 x3Z   x3X        
   x3u x3X         D3X # u3Z X3D         X3x u3x   
                      (Z3u)                        
     w3u         Z3u           u3Z         u3w     
x3x       x3Z   u3Z   U3x x3U   Z3u   Z3x       x3x
                                                   
  w3x   w3D   X3D   x3U     U3x   D3X   D3w   x3w  
                                                   
x3x       x3Z   u3Z   U3x x3U   Z3u   Z3x       x3x
     w3u         Z3u           u3Z         u3w     
                      (Z3u)                        
   x3u x3X         D3X # u3Z X3D         X3x u3x   
        X3x   Z3x                 x3Z   x3X        
                                                   
      u3x u3w   D3w Z3x     x3Z w3D   w3u x3u      
                                                   
                      (X3x)                        
         x3x x3w   u3w # x3X w3u   w3x x3x         
                                                   
               x3x   u3x   x3u   x3x

©

                      x3o   x3q   # o3w   q3x   o3x                      
                                 (w3o)                                   
                                                                         
             x3o         x3Q     o3Y Y3o     Q3x         o3x             
                                                                         
                                 (Y3q)                                   
          x3q   x3Q         w3Q   # q3Y   Q3w         Q3x   q3x          
                                                                         
                                                                         
       w3o         w3Q         A3o     o3A         Q3w         o3w       
      o3w   o3Y                 w3Y   Y3w                 Y3o   w3o      
                                                                         
          Y3o   Y3q   A3o                       o3A   q3Y   o3Y          
   q3x         q3Y     w3Y        xA3Ax        Y3w     Y3q         x3q   
                                                                         
                                                                         
o3x   Q3x   Q3w   # Y3w  xA3Ax             xA3Ax  # A3o   w3Q   x3Q   x3o
                 (o3A)                           (w3Y)                   
                                                                         
                                                                         
                                                                         
                 (o3A)                           (w3Y)                   
o3x   Q3x   Q3w   # Y3w  xA3Ax             xA3Ax  # A3o   w3Q   x3Q   x3o
                                                                         
                                                                         
   q3x         q3Y     w3Y        xA3Ax        Y3w     Y3q         x3q   
          Y3o   Y3q   A3o                       o3A   q3Y   o3Y          
                                                                         
      o3w   o3Y                 w3Y   Y3w                 Y3o   w3o      
       w3o         w3Q         A3o     o3A         Q3w         o3w       
                                                                         
                                                                         
          x3q   x3Q         w3Q   # q3Y   Q3w         Q3x   q3x          
                                 (Y3q)                                   
                                                                         
             x3o         x3Q     o3Y Y3o     Q3x         o3x             
                                                                         
                                 (w3o)                                   
                      x3o   x3q   # o3w   q3x   o3x

General of army (is itself convex)

Colonel of regiment

(is itself locally convex – uniform polychoral members:

by cells:	girco	hip	sirco	socco	toe	trip
sipti	24	48	48	24	24	96
prico	0	96	24	0	24	96

& others)

Confer

Grünbaumian relatives:: 2prico
segmentochora:: toe || girco
related CRFs:: gidpith

External
links

As abstract polytope prico is isomorphic to paqri, thereby replacing sirco by querco.

Diminishing the prico by toe-cupolae at hexadecachoral positions results in the gidpith.

Incidence matrix according to Dynkin symbol

x3x4o3x

. . . . | 576 |   1   2   2 |   2   2   1   2   1 |  1  2  1  1
--------+-----+-------------+---------------------+------------
x . . . |   2 | 288   *   * |   2   2   0   0   0 |  1  2  1  0
. x . . |   2 |   * 576   * |   1   0   1   1   0 |  1  1  0  1
. . . x |   2 |   *   * 576 |   0   1   0   1   1 |  0  1  1  1
--------+-----+-------------+---------------------+------------
x3x . . |   6 |   3   3   0 | 192   *   *   *   * |  1  1  0  0
x . . x |   4 |   2   0   2 |   * 288   *   *   * |  0  1  1  0
. x4o . |   4 |   0   4   0 |   *   * 144   *   * |  1  0  0  1
. x . x |   4 |   0   2   2 |   *   *   * 288   * |  0  1  0  1
. . o3x |   3 |   0   0   3 |   *   *   *   * 192 |  0  0  1  1
--------+-----+-------------+---------------------+------------
x3x4o . ♦  24 |  12  24   0 |   8   0   6   0   0 | 24  *  *  *
x3x . x ♦  12 |   6   6   6 |   2   3   0   3   0 |  * 96  *  *
x . o3x ♦   6 |   3   0   6 |   0   3   0   0   2 |  *  * 96  *
. x4o3x ♦  24 |   0  24  24 |   0   0   6  12   8 |  *  *  * 24

x3x4/3o3/2x

. .   .   . | 576 |   1   2   2 |   2   2   1   2   1 |  1  2  1  1
------------+-----+-------------+---------------------+------------
x .   .   . |   2 | 288   *   * |   2   2   0   0   0 |  1  2  1  0
. x   .   . |   2 |   * 576   * |   1   0   1   1   0 |  1  1  0  1
. .   .   x |   2 |   *   * 576 |   0   1   0   1   1 |  0  1  1  1
------------+-----+-------------+---------------------+------------
x3x   .   . |   6 |   3   3   0 | 192   *   *   *   * |  1  1  0  0
x .   .   x |   4 |   2   0   2 |   * 288   *   *   * |  0  1  1  0
. x4/3o   . |   4 |   0   4   0 |   *   * 144   *   * |  1  0  0  1
. x   .   x |   4 |   0   2   2 |   *   *   * 288   * |  0  1  0  1
. .   o3/2x |   3 |   0   0   3 |   *   *   *   * 192 |  0  0  1  1
------------+-----+-------------+---------------------+------------
x3x4/3o   . ♦  24 |  12  24   0 |   8   0   6   0   0 | 24  *  *  *
x3x   .   x ♦  12 |   6   6   6 |   2   3   0   3   0 |  * 96  *  *
x .   o3/2x ♦   6 |   3   0   6 |   0   3   0   0   2 |  *  * 96  *
. x4/3o3/2x ♦  24 |   0  24  24 |   0   0   6  12   8 |  *  *  * 24

s3s4x3x

demi( . . . . ) | 576 |   1   1   2   1 |  1   1   1   2   2  1 |  1  1  1  2
----------------+-----+-----------------+-----------------------+------------
demi( . . x . ) |   2 | 288   *   *   * |  1   0   1   1   0  0 |  1  0  1  1
demi( . . . x ) |   2 |   * 288   *   * |  1   0   0   0   2  1 |  0  1  1  2
sefa( s3s . . ) |   2 |   *   * 576   * |  0   1   0   1   1  0 |  1  1  0  1
sefa( . s4x . ) |   2 |   *   *   * 288 |  0   0   1   1   0  1 |  1  0  1  1
----------------+-----+-----------------+-----------------------+------------
demi( . . x3x ) |   6 |   3   3   0   0 | 96   *   *   *   *  * |  0  0  1  1
      s3s . .   ♦   3 |   0   0   3   0 |  * 192   *   *   *  * |  1  1  0  0
      . s4x .   ♦   4 |   2   0   0   2 |  *   * 144   *   *  * |  1  0  1  0
sefa( s3s4x . ) |   4 |   1   0   2   1 |  *   *   * 288   *  * |  1  0  0  1
sefa( s3s 2 x ) |   4 |   0   2   2   0 |  *   *   *   * 288  * |  0  1  0  1
sefa( . s4x3x ) |   6 |   0   3   0   3 |  *   *   *   *   * 96 |  0  0  1  1
----------------+-----+-----------------+-----------------------+------------
      s3s4x .   ♦  24 |  12   0  24  12 |  0   8   6  12   0  0 | 24  *  *  *
      s3s 2 x   ♦   6 |   0   3   6   0 |  0   2   0   0   3  0 |  * 96  *  *
      . s4x3x   ♦  24 |  12  12   0  12 |  4   0   6   0   0  4 |  *  * 24  *
sefa( s3s4x3x ) ♦  12 |   3   6   6   3 |  1   0   0   3   3  1 |  *  *  * 96

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