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W. Taylor (1977)
Varieties Obeying Homotopy LawsCanadian Journal of Mathematics, 29
G. Friedel
Etude sur les groupements cristallins
M. Nespolo, M. Aroyo (2016)
The crystallographic chameleon: when space groups change skin.Acta crystallographica. Section A, Foundations and advances, 72 Pt 5
Mathias Glatz, B. Stöger, K. Kirchner (2017)
Non-order–disorder allotwinning of the rhenium pincer complex cis-Re[(PNPCH2-iPr)(CO)2Cl]Acta Crystallographica Section B, Structural Science, Crystal Engineering and Materials, 73
Philipp Hans, B. Stöger, M. Weil, E. Zobetz (2015)
Structure of the mixed-metal carbonate KAgCO₃ revisited: order-disorder (OD) polytypism and allotwinning.Acta crystallographica Section B, Structural science, crystal engineering and materials, 71 Pt 2
R. Roth (1982)
Color symmetry and group theoryDiscret. Math., 38
Ronald Brown (1987)
From Groups to Groupoids: a Brief SurveyBulletin of The London Mathematical Society, 19
H. Brandt (1927)
Über eine Verallgemeinerung des GruppenbegriffesMathematische Annalen, 96
M. Marzouki, B. Souvignier, M. Nespolo (2013)
Analysis of the structural continuity in twinned crystals in terms of pseudo-eigensymmetry of crystallographic orbitsIUCrJ, 1
R. Sadanaga (1980)
Symmetry of superstructuresJournal of the Mineralogical Society of Japan, 14
M. Nespolo, G. Ferraris, B. Souvignier (2014)
Effects of merohedric twinning on the diffraction pattern.Acta crystallographica. Section A, Foundations and advances, 70 Pt 2
Daniel Strand, L. Folkers, S. Lidin (2016)
Allotwinning and OD-structures – the example of malonamideZeitschrift für Kristallographie - Crystalline Materials, 231
M. Nespolo, G. Ferraris, S. Ďurovič, Y. Takéuchi (2004)
Twins vs. modular crystal structuresZeitschrift für Kristallographie - Crystalline Materials, 219
M. Nespolo (2018)
Plesiotwins versus diperiodic twins.Acta crystallographica. Section A, Foundations and advances, 74 Pt 4
(1904)
Extrait du Bulletin de la Société de l'Industrie Minérale, Quatriè me sé rie, Tomes III et IV. Saint-É tienne: Societè de l'Imprimerie Thè olier
L. Royer (1954)
De l'épitaxie ; quelques remarques sur les problèmes qu'elle soulève, 77
W. Ledermann (1949)
Introduction to the theory of finite groups
C. Cayron (2006)
Groupoid of orientational variants.Acta crystallographica. Section A, Foundations of crystallography, 62 Pt 1
A. Shubnikov, V. Koptsik (1974)
Symmetry in Science and Art
M. Nespolo (2015)
Tips and traps on crystal twinning: how to fully describe your twinCrystal Research and Technology, 50
Paul Kautny, Thomas Schwartz, B. Stöger, J. Fröhlich (2017)
An unusual case of OD-allotwinning: 9,9′-(2,5-dibromo-1,4-phenylene)bis[9H-carbazole]Acta Crystallographica Section B, Structural Science, Crystal Engineering and Materials, 73
M. Nespolo, G. Ferraris, H. Takeda (2000)
Identification of two allotwins of mica polytypes in reciprocal space through the minimal rhombus unit.Acta crystallographica. Section B, Structural science, 56 Pt 4
M. Nespolo (2015)
The ash heap of crystallography: restoring forgotten basic knowledgeJournal of Applied Crystallography, 48
M. Nespolo (2004)
Twin point groups and the polychromatic symmetry of twinsZeitschrift für Kristallographie - Crystalline Materials, 219
Zuzana Hugonin, M. Johnsson, S. Lidin (2009)
Two for the price of one – Resolvable polymorphism in a ‘single crystal’ of α- and β-Sb3O4ISolid State Sciences, 11
M. Nespolo, T. Kogure (1998)
On the indexing of 3T mica polytypeZeitschrift Fur Kristallographie, 213
A. Guinier, G. Bokij, K. Boll-Dornberger, J. Cowley, S. D̂uroviĉ, H. Jagodzinski, P. Krishna, P. Wolff, B. Zvyagin, D. Cox, P. Goodman, T. Hahn, K. Kuchitsu, S. Abrahams (1984)
Nomenclature of Polytype Structures Report of the International Union of Crystallography Ad-Hoc Committee on the Nomenclature of Disordered, Modulated and Polytype Structures*Acta Crystallographica Section A, 40
M. Nespolo, B. Souvignier (2008)
Point groups in crystallography, 224
M. Nespolo, G. Ferraris (2004)
The oriented attachment mechanism in the formation of twins - a surveyEuropean Journal of Mineralogy, 16
O. Wittke, J. Garrido (1959)
Symétrie des polyèdres polychromatiques, 82
T. Hahn, V. Janovec, H. Klapper (1999)
Bicrystals, twins and domain structures – a comparisonFerroelectrics, 222
M. Nespolo, M. Aroyo (2016)
The modular structure of pyroxenesEuropean Journal of Mineralogy, 28
M. Nespolo, H. Takeda, G. Ferraris (1998)
Representation of the Axial Settings of Mica PolytypesActa Crystallographica Section A, 54
M. Nespolo, Giovanni Ferrarisb, H. Takedac (2000)
Twins and allotwins of basic mica polytypes: theoretical derivation and identification in the reciprocal spaceActa crystallographica. Section A, Foundations of crystallography, 56 (Pt 2)
M. Nespolo, T. Kogure, G. Ferraris (1999)
Allotwinning: oriented crystal association of polytypes - some warnings on consequencesZeitschrift Fur Kristallographie, 214
M. Nespolo, G. Ferraris, H. Takeda, Y. Takéuchi (1999)
Plesiotwinning: oriented crystal associations based on a large coincidence-site latticeZeitschrift Fur Kristallographie, 214
Carla Larvor, B. Stöger, M. Weil (2018)
The allotwinning of KCa3Te5O12Cl3: an OD interpretationZeitschrift für Kristallographie - Crystalline Materials, 233
A. Jahangiri, André Fleckhaus, S. Lidin, D. Strand (2013)
Allotwinning in a molecular crystal: (1R,3S)-dimethyl 2-oxocyclohexane-1,3-dicarboxylate.Acta crystallographica Section B, Structural science, crystal engineering and materials, 69 Pt 5
G. Friedel
Leçons de cristallographie
R. Danisi, T. Armbruster (2018)
Dehydration of microporous vanadosilicates: the case of VSH-13NaActa Crystallographica Section B Structural Science, Crystal Engineering and Materials
K. Dornberger‐Schiff (1979)
OD Structures, — a Game and a Bit MoreCrystal Research and Technology, 14
J. Dixon (1963)
General group extensionsPacific Journal of Mathematics, 13
The symmetry of twins is described by chromatic point groups obtained from the intersection group of the oriented point groups of the individuals extended by the operations mapping different individuals. This article presents a revised list of twin point groups through the analysis of their groupoid structure, followed by the generalization to the case of allotwins. Allotwins of polytypes with the same type of point group can be described by a chromatic point group like twins. If the individuals are all differently oriented, the chromatic point group is obtained in the same way as in the case of twins; if they are mapped by symmetry operation of the individuals, the chromatic point group is neutral. If the same holds true for some but not all individuals, then the allotwin can be seen as composed of twinned regions described by a twin point group, that are then allotwinned and described by a colour identification group; the allotwin is then described by a chromatic group obtained as an extension of the former by the latter, and requires the use of extended symbols reminiscent of the extended Hermann–Mauguin symbols of space groups. In the case of allotwins of polytypes with different types of point groups, as well as incomplete (allo)twins, a chromatic point group does not reveal the full symmetry: the groupoid has to be specified instead.
Acta Crystallographica Section A Foundations of Crystallography – Wiley
Published: May 1, 2019
Keywords: ; ; ; ;
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