TY - JOUR
T1 - Regular and defective vertex configurations in icosahedral structures
AU - Ben-Abraham, S. I.
AU - Baake, M.
AU - Kramer, P.
AU - Schlottmann, M.
N1 - Funding Information:
The authors would like to thank A. Joseph and D. Joseph for fruitful discussions and the Deutsche Forschungsgemeinschaft for financial support..
PY - 1993/2/2
Y1 - 1993/2/2
N2 - We have constructed all 5450 combinatorially possible vertex configurations formed by the Ammann rhombohedra. The defectiveness of the vertex configurations is quantified by a penalty functional defined as the minimal sum of squared distances between the dual acceptance domains for the constituent tiles of a given vertex. The vertices are then classified as ideal versus defective, quasiregular versus strictly forbidden, and regular versus singular. The classification is refined by defining rank as the dimension of the dual overlap and degree as the highest dimension of a facet violating the conditions of regularity.
AB - We have constructed all 5450 combinatorially possible vertex configurations formed by the Ammann rhombohedra. The defectiveness of the vertex configurations is quantified by a penalty functional defined as the minimal sum of squared distances between the dual acceptance domains for the constituent tiles of a given vertex. The vertices are then classified as ideal versus defective, quasiregular versus strictly forbidden, and regular versus singular. The classification is refined by defining rank as the dimension of the dual overlap and degree as the highest dimension of a facet violating the conditions of regularity.
UR - http://www.scopus.com/inward/record.url?scp=0027904725&partnerID=8YFLogxK
U2 - 10.1016/0022-3093(93)90329-V
DO - 10.1016/0022-3093(93)90329-V
M3 - Article
AN - SCOPUS:0027904725
SN - 0022-3093
VL - 153-154
SP - 132
EP - 136
JO - Journal of Non-Crystalline Solids
JF - Journal of Non-Crystalline Solids
IS - C
ER -