Finite spherical symmetry groups are also called point groups in three dimensions.
Grup simetri bola hingga juga disebut grup titik dalam tiga dimensi.
There are five fundamental symmetry classes which have triangular fundamental domains: dihedral, cyclic, tetrahedral, octahedral, and icosahedral symmetry.
Ada lima kelas simetri dasar yang memiliki domain dasar segitiga: dihedral, siklik, tetrahedral, oktahedral, dan simetri ikosahedral.
This article lists the groups by Schoenflies notation, Coxeter notation, orbifold notation, and order.
Artikel ini mencantumkan grup menurut notasi Schoenflies, notasi Coxeter, notasi orbifold, dan urutan.
John Conway used a variation of the Schoenflies notation, based on the groups' quaternion algebraic structure, labeled by one or two upper case letters, and whole number subscripts.
John Conway menggunakan variasi dari notasi Schoenflies, berdasarkan struktur aljabar grup kuaternion, diberikan label oleh satu atau dua huruf besar, dan subskrip bilangan bulat.
The group order is defined as the subscript, unless the order is doubled for symbols with a plus or minus, "±", prefix, which implies a central inversion.
Urutan grup didefinisikan sebagai subskrip, kecuali urutannya digandakan untuk simbol dengan plus atau minus, "±", awalan yang menyiratkan inversi pusat.
The crystallography groups, 32 in total, are a subset with element orders 2, 3, 4 and 6.
Grup kristalografi, total 32, adalah himpunan bagian dengan urutan elemen 2, 3, 4 dan 6.
There are four involutional groups: no symmetry (C1), reflection symmetry (Cs), 2-fold rotational symmetry (C2), and central point symmetry (Ci).
Ada empat grup involusial: tidak ada simetri (C1), simetri refleksi (Cs), Simetri rotasi lipatan 2 (C2), dan simetri titik pusat (Ci).
(n may be 1 as a special case as no symmetry)
(n mungkin 1 sebagai kasus khusus sebagai tidak simetri)
There are three infinite dihedral symmetry families, with n2 or higher (n may be 1 as a special case).
Ada tiga famili simetri dihedral tak hingga, dengan n2 atau tinggi (n mungkin 1 sebagai kasus khusus).
There are three types of polyhedral symmetry: tetrahedral symmetry, octahedral symmetry, and icosahedral symmetry, named after the triangle-faced regular polyhedra with these symmetries.
Ada tiga jenis simetri polihedral: simetri tetrahedral, simetri oktahedral, dan simetri ikosahedral, dinamai berdasarkan segitiga wajah polyhedra biasa dengan simetri ini.
Crystallographic point group Triangle group List of planar symmetry groups Point groups in two dimensions Peter R. Cromwell, Polyhedra (1997), Appendix I Sands, Donald E. (1993).
Grup titik kristalografi Grup segitiga Daftar grup simetri planar Grup titik dalam dua dimensiReferensi
ISBN 0-486-67839-3. On Quaternions and Octonions, 2003, John Horton Conway and Derek A. Smith ISBN 978-1-56881-134-5 The Symmetries of Things 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, ISBN 978-1-56881-220-5 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math.
ISBN 0-486-67839-3. On Quaternions and Octonions, 2003, John Horton Conway and Derek A. Smith ISBN 978-1-56881-134-5 The Symmetries of Things 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, ISBN 978-1-56881-220-5 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [2] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math.
3–45] N.W. Johnson: Geometries and Transformations, (2018) ISBN 978-1-107-10340-5 Chapter 11: Finite symmetry groups, Table 11.4 Finite Groups of Isometries in 3-space Finite spherical symmetry groups Weisstein, Eric W. "Schoenflies symbol".
3–45] N.W. Johnson: Geometries and Transformations, (2018) ISBN 978-1-107-10340-5 Chapter 11: Finite symmetry groups, Table 11.4 Finite Groups of Isometries in 3-space Finite spherical symmetry groups (Inggris) Weisstein, Eric W. "Schoenflies symbol".
Weisstein, Eric W. "Crystallographic point groups".
(Inggris) Weisstein, Eric W. "Crystallographic point groups".