Acronym cyted spic
Name cyclotetradiminished small prismatotetracontoctachoron
Circumradius sqrt[2+sqrt(2)] = 1.847759
Lace city
in approx. ASCII-art
x4o         x4x             x4x         x4o
  A           B               B           A
                                           
                                           
                    w4o                    
                      D                    
x4x         w4o             w4o         x4x
  B           C               C           B
                                           
                                           
        w4o         q4q         w4o        
          D           E           D        
                                           
                                           
x4x         w4o             w4o         x4x
  B           C               C           B
                    w4o                    
                      D                    
                                           
                                           
x4o         x4x             x4x         x4o
  A           B               B           A
Dihedral angles
  • at {4} between trip and trip:   arccos(-sqrt[8/9]) = 160.528779°
  • at {3} between oct and trip:   150°
  • at {3} between squippy and trip:   150°
  • at {4} between sirco and squippy:   135°
  • at {4} between sirco and trip:   arccos(-1/sqrt(3)) = 125.264390°
  • at {3} between oct and sirco:   120°
  • at {4} between sirco and sirco:   90°
Confer
segmentochora:
oct || sirco  
uniform relative:
spic   srit  

Diminishing spic by octasircoes at hexadecachoral positions results in the srit. Diminishing only at one cycle of 4 of those positions results in cyted spic. Accordingly cyted spic could also be obtained from srit by augmenting just a cycle of 4 of its sircoes by these caps.


Incidence matrix

16  *  *  * * |  2  4  0  0  0  0  0  0  0  0  0  0 | 1  4  2  2  0  0  0  0  0  0  0  0  0  0  0  0 | 2  2  1  0  0  0  0  0 0 0  (A) sirco-sirco connection vertices
 * 64  *  * * |  0  1  1  1  1  1  1  1  0  0  0  0 | 0  1  1  1  1  1  1  1  1  1  1  1  1  1  0  0 | 1  1  1  1  1  1  1  1 0 0  (B) non-connceting sirco vertices
 *  * 16  * * |  0  0  0  0  0  0  4  0  2  2  0  0 | 0  0  0  0  0  0  0  4  2  2  0  0  0  4  4  0 | 0  0  1  2  0  0  4  2 1 0  (C) non-sirco vertices of remaining pseudo tics
 *  *  * 16 * |  0  0  0  0  0  0  0  4  0  0  2  2 | 0  0  0  0  0  0  0  0  0  0  4  2  2  4  0  4 | 0  0  0  0  2  1  2  4 0 1  (D) vertices of reduced pseudo tics
 *  *  *  * 8 |  0  0  0  0  0  0  0  0  0  4  0  4 | 0  0  0  0  0  0  0  0  0  0  0  0  0  8  4  4 | 0  0  0  0  0  0  4  4 1 1  (E) vertices of remaining (q,x)-toe squares
--------------+-------------------------------------+------------------------------------------------+---------------------------
 2  0  0  0 0 | 16  *  *  *  *  *  *  *  *  *  *  * | 1  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0 | 2  1  0  0  0  0  0  0 0 0
 1  1  0  0 0 |  * 64  *  *  *  *  *  *  *  *  *  * | 0  1  1  1  0  0  0  0  0  0  0  0  0  0  0  0 | 1  1  1  0  0  0  0  0 0 0
 0  2  0  0 0 |  *  * 32  *  *  *  *  *  *  *  *  * | 0  0  0  0  1  1  0  1  0  0  0  1  0  0  0  0 | 1  0  0  1  0  1  1  0 0 0  para to cycle
 0  2  0  0 0 |  *  *  * 32  *  *  *  *  *  *  *  * | 0  0  1  0  1  0  0  0  1  0  0  0  0  0  0  0 | 1  0  1  1  0  0  0  0 0 0  perp to cycle, incident to sirco-{3}
 0  2  0  0 0 |  *  *  *  * 32  *  *  *  *  *  *  * | 0  1  0  0  0  1  1  0  0  0  0  0  1  0  0  0 | 1  1  0  0  1  1  0  0 0 0  perp to cycle, others
 0  2  0  0 0 |  *  *  *  *  * 32  *  *  *  *  *  * | 0  0  0  1  0  0  1  0  0  1  1  0  0  0  0  0 | 0  1  1  0  1  0  0  1 0 0  laterals of reduced sircoes
 0  1  1  0 0 |  *  *  *  *  *  * 64  *  *  *  *  * | 0  0  0  0  0  0  0  1  1  1  0  0  0  1  0  0 | 0  0  1  1  0  0  1  1 0 0  lacings of (b)-wedges
 0  1  0  1 0 |  *  *  *  *  *  *  * 64  *  *  *  * | 0  0  0  0  0  0  0  0  0  0  1  1  1  1  0  0 | 0  0  0  0  1  1  1  1 0 0  lacings of squippy
 0  0  2  0 0 |  *  *  *  *  *  *  *  * 16  *  *  * | 0  0  0  0  0  0  0  2  0  0  0  0  0  0  2  0 | 0  0  0  1  0  0  2  0 1 0  tops of (b)-wedges
 0  0  1  0 1 |  *  *  *  *  *  *  *  *  * 32  *  * | 0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  0 | 0  0  0  0  0  0  2  1 1 0
 0  0  0  2 0 |  *  *  *  *  *  *  *  *  *  * 16  * | 0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2 | 0  0  0  0  1  0  0  2 0 1
 0  0  0  1 1 |  *  *  *  *  *  *  *  *  *  *  * 32 | 0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2 | 0  0  0  0  0  0  1  2 0 1
--------------+-------------------------------------+------------------------------------------------+---------------------------
 4  0  0  0 0 |  4  0  0  0  0  0  0  0  0  0  0  0 | 4  *  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 2  0  0  0  0  0  0  0 0 0
 2  2  0  0 0 |  1  2  0  0  1  0  0  0  0  0  0  0 | * 32  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 1  1  0  0  0  0  0  0 0 0
 1  2  0  0 0 |  0  2  0  1  0  0  0  0  0  0  0  0 | *  * 32  *  *  *  *  *  *  *  *  *  *  *  *  * | 1  0  1  0  0  0  0  0 0 0  sirco-{3}
 1  2  0  0 0 |  0  2  0  0  0  1  0  0  0  0  0  0 | *  *  * 32  *  *  *  *  *  *  *  *  *  *  *  * | 0  1  1  0  0  0  0  0 0 0  sides of (a)-trips
 0  4  0  0 0 |  0  0  2  2  0  0  0  0  0  0  0  0 | *  *  *  * 16  *  *  *  *  *  *  *  *  *  *  * | 1  0  0  1  0  0  0  0 0 0  non-cubical sirco-{4}
 0  4  0  0 0 |  0  0  2  0  2  0  0  0  0  0  0  0 | *  *  *  *  * 16  *  *  *  *  *  *  *  *  *  * | 1  0  0  0  0  1  0  0 0 0  cubical sirco-{4}
 0  4  0  0 0 |  0  0  0  0  2  2  0  0  0  0  0  0 | *  *  *  *  *  * 16  *  *  *  *  *  *  *  *  * | 0  1  0  0  1  0  0  0 0 0  bases of (a)-trips
 0  2  2  0 0 |  0  0  1  0  0  0  2  0  1  0  0  0 | *  *  *  *  *  *  * 32  *  *  *  *  *  *  *  * | 0  0  0  1  0  0  1  0 0 0
 0  2  1  0 0 |  0  0  0  1  0  0  2  0  0  0  0  0 | *  *  *  *  *  *  *  * 32  *  *  *  *  *  *  * | 0  0  1  1  0  0  0  0 0 0  (b)-trip-{3}
 0  2  1  0 0 |  0  0  0  0  0  1  2  0  0  0  0  0 | *  *  *  *  *  *  *  *  * 32  *  *  *  *  *  * | 0  0  1  0  0  0  0  1 0 0  oct-incident
 0  2  0  2 0 |  0  0  0  0  0  1  0  2  0  0  1  0 | *  *  *  *  *  *  *  *  *  * 32  *  *  *  *  * | 0  0  0  0  1  0  0  1 0 0
 0  2  0  1 0 |  0  0  1  0  0  0  0  2  0  0  0  0 | *  *  *  *  *  *  *  *  *  *  * 32  *  *  *  * | 0  0  0  0  0  1  1  0 0 0  para to cycle
 0  2  0  1 0 |  0  0  0  0  1  0  0  2  0  0  0  0 | *  *  *  *  *  *  *  *  *  *  *  * 32  *  *  * | 0  0  0  0  1  1  0  0 0 0  perp to cycle
 0  1  1  1 1 |  0  0  0  0  0  0  1  1  0  1  0  1 | *  *  *  *  *  *  *  *  *  *  *  *  * 64  *  * | 0  0  0  0  0  0  1  1 0 0
 0  0  2  0 1 |  0  0  0  0  0  0  0  0  1  2  0  0 | *  *  *  *  *  *  *  *  *  *  *  *  *  * 32  * | 0  0  0  0  0  0  1  0 1 0
 0  0  0  2 1 |  0  0  0  0  0  0  0  0  0  0  1  2 | *  *  *  *  *  *  *  *  *  *  *  *  *  *  * 32 | 0  0  0  0  0  0  0  1 0 1
--------------+-------------------------------------+------------------------------------------------+---------------------------
 8 16  0  0 0 |  8 16  8  8  8  0  0  0  0  0  0  0 | 2  8  8  0  4  4  0  0  0  0  0  0  0  0  0  0 | 4  *  *  *  *  *  *  * * *  sirco
 2  4  0  0 0 |  1  4  0  0  2  2  0  0  0  0  0  0 | 0  2  0  2  0  0  1  0  0  0  0  0  0  0  0  0 | * 16  *  *  *  *  *  * * *  trip (a)
 1  4  1  0 0 |  0  4  0  2  0  2  4  0  0  0  0  0 | 0  0  2  2  0  0  0  0  2  2  0  0  0  0  0  0 | *  * 16  *  *  *  *  * * *  oct
 0  4  2  0 0 |  0  0  2  2  0  0  4  0  1  0  0  0 | 0  0  0  0  1  0  0  2  2  0  0  0  0  0  0  0 | *  *  * 16  *  *  *  * * *  trip (b)
 0  4  0  2 0 |  0  0  0  0  2  2  0  4  0  0  1  0 | 0  0  0  0  0  0  1  0  0  0  2  0  2  0  0  0 | *  *  *  * 16  *  *  * * *  trip
 0  4  0  1 0 |  0  0  2  0  2  0  0  4  0  0  0  0 | 0  0  0  0  0  1  0  0  0  0  0  2  2  0  0  0 | *  *  *  *  * 16  *  * * *  squippy
 0  2  2  1 1 |  0  0  1  0  0  0  2  2  1  2  0  1 | 0  0  0  0  0  0  0  1  0  0  0  1  0  2  1  0 | *  *  *  *  *  * 32  * * *  trip
 0  2  1  2 1 |  0  0  0  0  0  1  2  2  0  1  1  2 | 0  0  0  0  0  0  0  0  0  1  1  0  0  2  0  1 | *  *  *  *  *  *  * 32 * *  trip
 0  0  4  0 2 |  0  0  0  0  0  0  0  0  4  8  0  0 | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  0 | *  *  *  *  *  *  *  * 4 *  oct
 0  0  0  4 2 |  0  0  0  0  0  0  0  0  0  0  4  8 | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8 | *  *  *  *  *  *  *  * * 4  oct

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