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Jerusalem cross based on a cross potent (as commonly realised in early modern heraldry) The national flag of Georgia The Jerusalem cross (also known as "five-fold Cross", or "cross-and-crosslets") is a heraldic cross and Christian cross variant consisting of a large cross potent surrounded by four smaller Greek crosses, one in each quadrant, representing the Four Evangelists and the spread of ...
Thus 5-fold rotational symmetry cannot be eliminated by an argument missing either of those assumptions. A Penrose tiling of the whole (infinite) plane can only have exact 5-fold rotational symmetry (of the whole tiling) about a single point, however, whereas the 4-fold and 6-fold lattices have infinitely many centres of rotational symmetry.
The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions.
The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals: implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its tiles ...
In another definition of the word, the rotation group of an object is the symmetry group within E + (n), the group of direct isometries; in other words, the intersection of the full symmetry group and the group of direct isometries. For chiral objects it is the same as the full symmetry group.
The Fivefold Scapular, also known as Redemptorist Scapular, is a sacramental made up of five best-known of the early scapulars in the Catholic Church: the Brown Scapular of the Carmelites, the Blue Scapular of the Immaculate Conception, the Black Scapular of the Servites, the Red Scapular of the Passion, and the White Scapular of the Most Holy Trinity.
The full title was A Dictionary of the Bible, dealing with the Language, Literature and Contents, including the Biblical Theology. It was edited by James Hastings, with the assistance of John A. Selbie. Additional assistance with revision of the proofs was provided by A. B. Davidson, S. R. Driver and H. B. Swete. Four volumes (1898—1902 ...
Pancikarana is the "quintuplication" of the basic/primordial five subtle elements. The subtle elements stand alone ( tanmātrā ). During pancikarana , each is firstly divided into two halves, one part of which was further divided into four parts, equal to 1/8 parts of each subtle element, which then recombined with the undivided halves of each ...