Acronym stawros
Name pentagrammic ({10} || pip-)wedge rosette,
bridge cyclopentaaugmented starpedip,
ring-augmented starpedip
Lace city
in approx. ASCII-art
         x5o         
                     
                     
x5o               x5o
                     
         x5x         
                     
                     
                     
    x5o       x5o    
Dihedral angles
  • at {3} between tet and trip:   arccos(-sqrt[9+3 sqrt(5)]/4) = 172.238756°
  • at {4} between pip and trip:   arccos(-sqrt[(10+2 sqrt(5))/15]) = 169.187683°
  • at {3} between tet and tet:   arccos[(3 sqrt(5)-1)/8] = 44.477512°
  • at {4} between trip and trip:   arccos(sqrt(5)/3) = 41.810315°
  • at {5} between pip and pip:   36°
Pattern
A-------A-------A-------A-------A------(A)
|\     /|\     /|\     /|\     /|\     /
--B---B---B---B---B---B---B---B---B---B--
|/     \|/     \|/     \|/     \|/     \
A-------A-------A-------A-------A------(A)
|\     /|\     /|\     /|\     /|\     /
--B---B---B---B---B---B---B---B---B---B--
|/     \|/     \|/     \|/     \|/     \
A-------A-------A-------A-------A------(A)
|\     /|\     /|\     /|\     /|\     /
--B---B---B---B---B---B---B---B---B---B--
|/     \|/     \|/     \|/     \|/     \
A-------A-------A-------A-------A------(A)
|\     /|\     /|\     /|\     /|\     /
--B---B---B---B---B---B---B---B---B---B--
|/     \|/     \|/     \|/     \|/     \
A-------A-------A-------A-------A------(A)
|\     /|\     /|\     /|\     /|\     /
--B---B---B---B---B---B---B---B---B---B--
|/     \|/     \|/     \|/     \|/     \
(A)    (A)     (A)     (A)     (A)     (A)

vertical -B-B- lines to be identified
Confer
related segmentochora:
{10} || pip  
augmentation base:
starpedip  
related CRFs:
quawros  

This non-orbiform, non-convex polychoron could be constructed by augmenting the stips of a starpedip (represented as vertices A in the pattern) by stappyps (as line||stip wedges). Further the gaps between these augmentations get bridged by further filled in stappypies. – Thereby the pentagrams (projected onto the vertical A-A-connections in the pattern above) finally will be withdrawn likewise.

Alternatively this polychoron could be constructed by attaching 5 {10} || pip segmentochora around the decagon (represented by the B vertices in the pattern above – running twice around), pairwise blending out the pecues.


Incidence matrix

(according to pattern)

25  * |  2  2  2 0 0 | 1  4  2  4  1 | 2  4  2  (A)
 * 10 |  0  0  5 1 1 | 0  0  5  5  5 | 0  5  5  (B)
------+--------------+---------------+--------
 2  0 | 25  *  * * * | 1  2  1  0  0 | 2  2  0  horizontal
 2  0 |  * 25  * * * | 0  2  0  2  0 | 1  2  1  vertical
 1  1 |  *  * 50 * * | 0  0  1  2  1 | 0  2  2
 0  2 |  *  *  * 5 * | 0  0  5  0  0 | 0  5  0  inc. to trip
 0  2 |  *  *  * * 5 | 0  0  0  0  5 | 0  0  5  inc. to tet
------+--------------+---------------+--------
 5  0 |  5  0  0 0 0 | 5  *  *  *  * | 2  0  0  {5}
 4  0 |  2  2  0 0 0 | * 25  *  *  * | 1  1  0
 2  2 |  1  0  2 1 0 | *  * 25  *  * | 0  2  0
 2  1 |  0  1  2 0 0 | *  *  * 50  * | 0  1  1
 1  2 |  0  0  2 0 1 | *  *  *  * 25 | 0  0  2
------+--------------+---------------+--------
10  0 | 10  5  0 0 0 | 2  5  0  0  0 | 5  *  *  pip
 4  2 |  2  2  4 1 0 | 0  1  2  2  0 | * 25  *  trip
 2  2 |  0  1  4 0 1 | 0  0  0  2  2 | *  * 25  tet

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