Acronym stawros Name pentagrammic ({10} || pip-)wedge rosette,bridge cyclopentaaugmented starpedip,ring-augmented starpedip Lace cityin 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 – Thereby the pentagrams (projected onto the vertical A-A-connections in the pattern above) finally will be withdrawn likewise.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