Acronym ...
Name (1,0,4,12,0)-diminished vertex-first-rotunda of ex,
heptadeca-diminished vertex-first rotunda of hexacosachoron
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art
        x3o   o3f f3o   o3x        
                                   
                                   
     o3f   f3x  demi(x3f)  f3o o3o 
                                   
                                       (F=ff)
                                   
                                   
o3x   x3f F3o   f3f   o3F f3x   x3o
Confer
segmentochora:
ike || doe   doe || id  
other CRFs:
rotunda of ex   pt || ike || doe || id   ike || doe || id   ike || cube-dim-doe || id  
uniform relative:
ex  

The medial section here is the tetrahedrally diminished dodecahedron. From that section the whole polychoron inherits its chirality.


Incidence matrix

ike || pseudo tet-dim-doe || id   → height(1,2) = 1/2, height(2,3) = (1+sqrt(5))/4 = 0.809017

12  * *  * *  * |  2 1  2  1  1  1  1 0  0  0  0  0  0  0  0  0  0  0 | 1  3 1  2  2  2  2  1  1  1  1 0  0  0  0  0  0 0  0  0 0 | 1 1  3 1 1  2  1  0 0 0  all ike level vertices
 * 12 *  * *  * |  0 0  0  1  1  1  0 1  1  1  1  1  0  0  0  0  0  0 | 0  0 0  1  1  1  0  2  2  1  1 1  1  1  1  1  0 0  0  0 0 | 0 1  1 0 1  1  3  1 0 0  B-doe / dim.vertices of doe level
 *  * 4  * *  * |  0 0  0  0  0  0  3 0  3  0  0  0  3  0  0  0  0  0 | 0  0 0  0  0  0  3  0  0  3  3 0  3  0  0  0  3 0  0  0 0 | 0 0  0 1 0  3  3  0 1 0  C-doe / isol. vertices of doe level, verf: teddi
 *  * * 12 *  * |  0 0  0  0  0  0  0 0  0  1  0  0  0  2  1  1  0  0 | 0  0 0  0  0  0  0  2  0  0  0 0  0  1  1  0  0 1  2  1 0 | 0 1  0 0 0  0  2  1 0 1  A-id / tetrahedral triangle vertices of id level
 *  * *  * 6  * |  0 0  0  0  0  0  0 0  0  0  2  0  0  0  2  0  2  0 | 0  0 0  0  0  0  0  0  0  0  0 1  0  2  0  2  0 0  2  2 0 | 0 0  0 0 0  0  2  2 0 1  B-id / isol. / octahedral vertices of id level
 *  * *  * * 12 |  0 0  0  0  0  0  0 0  0  0  0  1  1  0  0  1  1  2 | 0  0 0  0  0  0  0  0  0  0  0 0  1  0  1  1  2 0  2  1 1 | 0 0  0 0 0  0  2  1 1 1  C-id / other tetrahedral triangle vertices of id level
----------------+-----------------------------------------------------+-----------------------------------------------------------+------------------------
 2  0 0  0 0  0 | 12 *  *  *  *  *  * *  *  *  *  *  *  *  *  *  *  * | 1  1 0  1  0  0  0  0  0  0  0 0  0  0  0  0  0 0  0  0 0 | 1 1  1 0 0  0  0  0 0 0  A/B-edge of ike layer
 2  0 0  0 0  0 |  * 6  *  *  *  *  * *  *  *  *  *  *  *  *  *  *  * | 0  2 0  0  2  0  0  0  0  0  0 0  0  0  0  0  0 0  0  0 0 | 1 0  2 0 1  0  0  0 0 0  B/B-edge of ike layer
 2  0 0  0 0  0 |  * * 12  *  *  *  * *  *  *  *  *  *  *  *  *  *  * | 0  1 1  0  0  1  1  0  0  0  0 0  0  0  0  0  0 0  0  0 0 | 1 0  1 1 0  1  0  0 0 0  B/C-edge of ike layer
 1  1 0  0 0  0 |  * *  * 12  *  *  * *  *  *  *  *  *  *  *  *  *  * | 0  0 0  1  1  0  0  1  1  0  0 0  0  0  0  0  0 0  0  0 0 | 0 1  1 0 1  0  1  0 0 0  with adj. {5}, near bottom B vertex of doe-layer trapezium
 1  1 0  0 0  0 |  * *  *  * 12  *  * *  *  *  *  *  *  *  *  *  *  * | 0  0 0  1  0  1  0  1  0  1  0 0  0  0  0  0  0 0  0  0 0 | 0 1  1 0 0  1  1  0 0 0  with adj. {5}, near bottom C vertex of doe-layer trapezium
 1  1 0  0 0  0 |  * *  *  *  * 12  * *  *  *  *  *  *  *  *  *  *  * | 0  0 0  0  1  1  0  0  1  0  1 0  0  0  0  0  0 0  0  0 0 | 0 0  1 0 1  1  1  0 0 0  w/o adj. {5}
 1  0 1  0 0  0 |  * *  *  *  *  * 12 *  *  *  *  *  *  *  *  *  *  * | 0  0 0  0  0  0  2  0  0  1  1 0  0  0  0  0  0 0  0  0 0 | 0 0  0 1 0  2  1  0 0 0
 0  2 0  0 0  0 |  * *  *  *  *  *  * 6  *  *  *  *  *  *  *  *  *  * | 0  0 0  0  0  0  0  0  2  0  0 1  0  0  0  0  0 0  0  0 0 | 0 0  0 0 1  0  2  0 0 0
 0  1 1  0 0  0 |  * *  *  *  *  *  * * 12  *  *  *  *  *  *  *  *  * | 0  0 0  0  0  0  0  0  0  1  1 0  1  0  0  0  0 0  0  0 0 | 0 0  0 0 0  1  2  0 0 0
 0  1 0  1 0  0 |  * *  *  *  *  *  * *  * 12  *  *  *  *  *  *  *  * | 0  0 0  0  0  0  0  2  0  0  0 0  0  1  1  0  0 0  0  0 0 | 0 1  0 0 0  0  2  1 0 0
 0  1 0  0 1  0 |  * *  *  *  *  *  * *  *  * 12  *  *  *  *  *  *  * | 0  0 0  0  0  0  0  0  0  0  0 1  0  1  0  1  0 0  0  0 0 | 0 0  0 0 0  0  2  1 0 0
 0  1 0  0 0  1 |  * *  *  *  *  *  * *  *  *  * 12  *  *  *  *  *  * | 0  0 0  0  0  0  0  0  0  0  0 0  1  0  1  1  0 0  0  0 0 | 0 0  0 0 0  0  2  1 0 0
 0  0 1  0 0  1 |  * *  *  *  *  *  * *  *  *  *  * 12  *  *  *  *  * | 0  0 0  0  0  0  0  0  0  0  0 0  1  0  0  0  2 0  0  0 0 | 0 0  0 0 0  0  2  0 1 0
 0  0 0  2 0  0 |  * *  *  *  *  *  * *  *  *  *  *  * 12  *  *  *  * | 0  0 0  0  0  0  0  1  0  0  0 0  0  0  0  0  0 1  1  0 0 | 0 1  0 0 0  0  1  0 0 1
 0  0 0  1 1  0 |  * *  *  *  *  *  * *  *  *  *  *  *  * 12  *  *  * | 0  0 0  0  0  0  0  0  0  0  0 0  0  1  0  0  0 0  1  1 0 | 0 0  0 0 0  0  1  1 0 1
 0  0 0  1 0  1 |  * *  *  *  *  *  * *  *  *  *  *  *  *  * 12  *  * | 0  0 0  0  0  0  0  0  0  0  0 0  0  0  1  0  0 0  1  1 0 | 0 0  0 0 0  0  1  1 0 1
 0  0 0  0 1  1 |  * *  *  *  *  *  * *  *  *  *  *  *  *  *  * 12  * | 0  0 0  0  0  0  0  0  0  0  0 0  0  0  0  1  0 0  1  1 0 | 0 0  0 0 0  0  1  1 0 1
 0  0 0  0 0  2 |  * *  *  *  *  *  * *  *  *  *  *  *  *  *  *  * 12 | 0  0 0  0  0  0  0  0  0  0  0 0  0  0  0  0  1 0  1  0 1 | 0 0  0 0 0  0  1  0 1 1
----------------+-----------------------------------------------------+-----------------------------------------------------------+------------------------
 3  0 0  0 0  0 |  3 0  0  0  0  0  0 0  0  0  0  0  0  0  0  0  0  0 | 4  * *  *  *  *  *  *  *  *  * *  *  *  *  *  * *  *  * * | 1 1  0 0 0  0  0  0 0 0  A-{3} of ike layer
 3  0 0  0 0  0 |  1 1  1  0  0  0  0 0  0  0  0  0  0  0  0  0  0  0 | * 12 *  *  *  *  *  *  *  *  * *  *  *  *  *  * *  *  * * | 1 0  1 0 0  0  0  0 0 0  B-{3} of ike layer
 3  0 0  0 0  0 |  0 0  3  0  0  0  0 0  0  0  0  0  0  0  0  0  0  0 | *  * 4  *  *  *  *  *  *  *  * *  *  *  *  *  * *  *  * * | 1 0  0 1 0  0  0  0 0 0  C-{3} of ike layer
 2  1 0  0 0  0 |  1 0  0  1  1  0  0 0  0  0  0  0  0  0  0  0  0  0 | *  * * 12  *  *  *  *  *  *  * *  *  *  *  *  * *  *  * * | 0 1  1 0 0  0  0  0 0 0  dangling from A/B-edge of ike layer
 2  1 0  0 0  0 |  0 1  0  1  0  1  0 0  0  0  0  0  0  0  0  0  0  0 | *  * *  * 12  *  *  *  *  *  * *  *  *  *  *  * *  *  * * | 0 0  1 0 1  0  0  0 0 0  dangling from B/B-edge of ike layer
 2  1 0  0 0  0 |  0 0  1  0  1  1  0 0  0  0  0  0  0  0  0  0  0  0 | *  * *  *  * 12  *  *  *  *  * *  *  *  *  *  * *  *  * * | 0 0  1 0 0  1  0  0 0 0  dangling from B/C-edge of ike layer
 2  0 1  0 0  0 |  0 0  1  0  0  0  2 0  0  0  0  0  0  0  0  0  0  0 | *  * *  *  *  * 12  *  *  *  * *  *  *  *  *  * *  *  * * | 0 0  0 1 0  1  0  0 0 0
 1  2 0  2 0  0 |  0 0  0  1  1  0  0 0  0  2  0  0  0  1  0  0  0  0 | *  * *  *  *  *  * 12  *  *  * *  *  *  *  *  * *  *  * * | 0 1  0 0 0  0  1  0 0 0  lacing {5}
 1  2 0  0 0  0 |  0 0  0  1  0  1  0 1  0  0  0  0  0  0  0  0  0  0 | *  * *  *  *  *  *  * 12  *  * *  *  *  *  *  * *  *  * * | 0 0  0 0 1  0  1  0 0 0
 1  1 1  0 0  0 |  0 0  0  0  1  0  1 0  1  0  0  0  0  0  0  0  0  0 | *  * *  *  *  *  *  *  * 12  * *  *  *  *  *  * *  *  * * | 0 0  0 0 0  1  1  0 0 0  above bottom B/C-edge of doe-layer trapezium
 1  1 1  0 0  0 |  0 0  0  0  0  1  1 0  1  0  0  0  0  0  0  0  0  0 | *  * *  *  *  *  *  *  *  * 12 *  *  *  *  *  * *  *  * * | 0 0  0 0 0  1  1  0 0 0  above lateral B/C-edge of doe-layer trapezium
 0  2 0  0 1  0 |  0 0  0  0  0  0  0 1  0  0  2  0  0  0  0  0  0  0 | *  * *  *  *  *  *  *  *  *  * 6  *  *  *  *  * *  *  * * | 0 0  0 0 0  0  2  0 0 0
 0  1 1  0 0  1 |  0 0  0  0  0  0  0 0  1  0  0  1  1  0  0  0  0  0 | *  * *  *  *  *  *  *  *  *  * * 12  *  *  *  * *  *  * * | 0 0  0 0 0  0  2  0 0 0
 0  1 0  1 1  0 |  0 0  0  0  0  0  0 0  0  1  1  0  0  0  1  0  0  0 | *  * *  *  *  *  *  *  *  *  * *  * 12  *  *  * *  *  * * | 0 0  0 0 0  0  1  1 0 0
 0  1 0  1 0  1 |  0 0  0  0  0  0  0 0  0  1  0  1  0  0  0  1  0  0 | *  * *  *  *  *  *  *  *  *  * *  *  * 12  *  * *  *  * * | 0 0  0 0 0  0  1  1 0 0
 0  1 0  0 1  1 |  0 0  0  0  0  0  0 0  0  0  1  1  0  0  0  0  1  0 | *  * *  *  *  *  *  *  *  *  * *  *  *  * 12  * *  *  * * | 0 0  0 0 0  0  1  1 0 0
 0  0 1  0 0  2 |  0 0  0  0  0  0  0 0  0  0  0  0  2  0  0  0  0  1 | *  * *  *  *  *  *  *  *  *  * *  *  *  *  * 12 *  *  * * | 0 0  0 0 0  0  1  0 1 0
 0  0 0  3 0  0 |  0 0  0  0  0  0  0 0  0  0  0  0  0  3  0  0  0  0 | *  * *  *  *  *  *  *  *  *  * *  *  *  *  *  * 4  *  * * | 0 1  0 0 0  0  0  0 0 1
 0  0 0  2 1  2 |  0 0  0  0  0  0  0 0  0  0  0  0  0  1  1  1  1  1 | *  * *  *  *  *  *  *  *  *  * *  *  *  *  *  * * 12  * * | 0 0  0 0 0  0  1  0 0 1  bottom {5}
 0  0 0  1 1  1 |  0 0  0  0  0  0  0 0  0  0  0  0  0  0  1  1  1  0 | *  * *  *  *  *  *  *  *  *  * *  *  *  *  *  * *  * 12 * | 0 0  0 0 0  0  0  1 0 1
 0  0 0  0 0  3 |  0 0  0  0  0  0  0 0  0  0  0  0  0  0  0  0  0  3 | *  * *  *  *  *  *  *  *  *  * *  *  *  *  *  * *  *  * 4 | 0 0  0 0 0  0  0  0 1 1
----------------+-----------------------------------------------------+-----------------------------------------------------------+------------------------
12  0 0  0 0  0 | 12 6 12  0  0  0  0 0  0  0  0  0  0  0  0  0  0  0 | 4 12 4  0  0  0  0  0  0  0  0 0  0  0  0  0  0 0  0  0 0 | 1 *  * * *  *  *  * * *  ike (top layer)
 3  3 0  3 0  0 |  3 0  0  3  3  0  0 0  0  3  0  0  0  3  0  0  0  0 | 1  0 0  3  0  0  0  3  0  0  0 0  0  0  0  0  0 1  0  0 0 | * 4  * * *  *  *  * * *  teddi (A vertical)
 3  1 0  0 0  0 |  1 1  1  1  1  1  0 0  0  0  0  0  0  0  0  0  0  0 | 0  1 0  1  1  1  0  0  0  0  0 0  0  0  0  0  0 0  0  0 0 | * * 12 * *  *  *  * * *  tet (upper B vertical)
 3  0 1  0 0  0 |  0 0  3  0  0  0  3 0  0  0  0  0  0  0  0  0  0  0 | 0  0 1  0  0  0  3  0  0  0  0 0  0  0  0  0  0 0  0  0 0 | * *  * 4 *  *  *  * * *  tet (upper C vertical)
 2  2 0  0 0  0 |  0 1  0  2  0  2  0 1  0  0  0  0  0  0  0  0  0  0 | 0  0 0  0  2  0  0  0  2  0  0 0  0  0  0  0  0 0  0  0 0 | * *  * * 6  *  *  * * *  tet (underneath top B/B-edge)
 2  1 1  0 0  0 |  0 0  1  0  1  1  2 0  1  0  0  0  0  0  0  0  0  0 | 0  0 0  0  0  1  1  0  0  1  1 0  0  0  0  0  0 0  0  0 0 | * *  * * * 12  *  * * *  tet (underneath top B/C-edge)
 1  3 1  2 1  2 |  0 0  0  1  1  1  1 1  2  2  2  2  2  1  1  1  1  1 | 0  0 0  0  0  0  0  1  1  1  1 1  2  1  1  1  1 0  1  0 0 | * *  * * *  * 12  * * *  mibdi
 0  1 0  1 1  1 |  0 0  0  0  0  0  0 0  0  1  1  1  0  0  1  1  1  0 | 0  0 0  0  0  0  0  0  0  0  0 0  0  1  1  1  0 0  0  1 0 | * *  * * *  *  * 12 * *  tet (atop bottom ABC {3})
 0  0 1  0 0  3 |  0 0  0  0  0  0  0 0  0  0  0  0  3  0  0  0  0  1 | 0  0 0  0  0  0  0  0  0  0  0 0  0  0  0  0  3 0  0  0 1 | * *  * * *  *  *  * 4 *  tet (lower C vertical)
 0  0 0 12 6 12 |  0 0  0  0  0  0  0 0  0  0  0  0  0 12 12 12 12 12 | 0  0 0  0  0  0  0  0  0  0  0 0  0  0  0  0  0 4 12 12 4 | * *  * * *  *  *  * * 1  id (bottom layer)

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