In three dimensional geometry, there are four infinite series of point groups in three dimensions (n ≥ 1) with n-fold rotational or reflectional symmetry about one axis (by an angle of 360°/n) that does not change the object.
Dalam geometri tiga dimensi, empat deret tak hingga grup titik dalam tiga dimensi (n≥1) dengan lipatan-n simetri rotasi atau refleksi pada satu sumbu (dengan sudut 360°/n)
Cnv, [n], (*nn) of order 2n - pyramidal symmetry or full acro-n-gonal group (abstract group Dihn); in biology C2v is called biradial symmetry.
Ia memiliki simetri refleksi berhubungan dengan bidang yang tegak lurus terhadap sumbu rotasi lipatan n. Cnv, [n], (*nn) urutan 2n - simetri piramida atau grup akro-n-gonal penuh (grup abstrak Dihn); dalam biologi C2v disebut juga sebagai simetri biradial.
For n1 we have again Cs (1*).
Untuk n=1 memiliki Cs (1*).
This is the symmetry group for a regular n-sided pyramid.
Ini adalah grup simetri untuk sisi-n piramida beraturan.
S2n, [2+,2n+], (n×) of order 2n - gyro-n-gonal group (not to be confused with symmetric groups, for which the same notation is used; abstract group Z2n); It has a 2n-fold rotoreflection axis, also called 2n-fold improper rotation axis, i.e., the symmetry group contains a combination of a reflection in the horizontal plane and a rotation by an angle 180°/n.
S2n, [2+,2n+], (n×) urutan 2n - grup giro-n-gonal (jangan disamakan dengan grup simetris, yang notasinya sama digunakan; grup abstrak Z2n); Ini memiliki sumbu lipatan-2n rotorefleksi, juga disebut sumbu rotasi tak wajar lipatan-2n, yaitu grup simetri berisi kombinasi pantulan pada bidang horizontal dan rotasi dengan sudut 180°/n.
C2h, [2,2+] (2*) and C2v, [2], (*22) of order 4 are two of the three 3D symmetry group types with the Klein four-group as abstract group.
C2h, [2,2+] (2*) dan C2v, [2], (*22) urutan 4 adalah dua dari tiga jenis grup simetri 3D dengan Grup empat Klein sebagai grup abstrak.
Dihedral symmetry in three dimensions Sands, Donald E. (1993).
Simetri dihedral dalam tiga dimensi Sands, Donald E. (1993).
Mineola, New York: Dover Publications, Inc. p. 165.
Mineola, New York: Dover Publications, Inc. hlm. 165.
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, wiley.com, ISBN 978-0-471-01003-6 N.W. Johnson: Geometries and Transformations, (2018)
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 [1] N.W. Johnson: Geometries and Transformations, (2018)
ISBN 978-1-107-10340-5, Chapter 11: Finite symmetry groups, 11.5 Spherical Coxeter groups
ISBN 978-1-107-10340-5 Chapter 11: Finite symmetry groups, 11.5 Spherical Coxeter groups