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Hexagram
, can be seen as a compound polygon, compound composed of an upwards (blue here) and downwards (pink) facing equilateral triangle, with their intersection as a regular hexagon (in green). A hexagram (Greek language, Greek) or sexagram (Latin language, Latin) is a six-pointed geometric star figure with the Schläfli symbol , 2, or . The term is used to refer to a compound figure of two equilateral triangles. The intersection is a regular hexagon. The hexagram is part of an infinite series of shapes which are compounds of two n-dimensional simplex, simplices. In three dimensions, Compound of two tetrahedra, the analogous compound is the stellated octahedron, and in four dimensions the compound of two 5-cells is obtained. It has been historically used in various religious and cultural contexts and as decorative motifs. The symbol was used as a decorative motif in medieval Christian churches and Jewish synagogues. In the medieval period, a Muslim mystical symbol known as the Seal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagon
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A regular hexagon is defined as a hexagon that is both equilateral and equiangular. In other words, a hexagon is said to be regular if the edges are all equal in length, and each of its internal angle is equal to 120°. The Schläfli symbol denotes this polygon as \ . However, the regular hexagon can also be considered as the cutting off the vertices of an equilateral triangle, which can also be denoted as \mathrm\ . A regular hexagon is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals \tfrac times the apothem (radius of the inscribed circle). Measurement The longest diagonals of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schläfli Symbol
In geometry, the Schläfli symbol is a notation of the form \ that defines List of regular polytopes and compounds, regular polytopes and tessellations. The Schläfli symbol is named after the 19th-century Swiss mathematician Ludwig Schläfli, who generalized Euclidean space, Euclidean geometry to more than three dimensions and discovered all their convex regular polytopes, including the six that occur in four dimensions. Definition The Schläfli symbol is a Recursive definition, recursive description, starting with \ for a p-sided regular polygon that is Convex set, convex. For example, is an equilateral triangle, is a Square (geometry), square, a convex regular pentagon, etc. Regular star polygons are not convex, and their Schläfli symbols \ contain irreducible fractions p/q, where p is the number of vertices, and q is their turning number. Equivalently, \ is created from the vertices of \, connected every q. For example, \ is a pentagram; \ is a pentagon. A regular pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yantra
Yantra (; 'machine'/'contraption') is a geometrical diagram, mainly from the Tantric traditions of the Indian religions. Yantras are used for the worship of deities in temples or at home; as an aid in meditation; and for the benefits believed given by their occult powers based on Hindu astrology and tantric texts. They are also used for adornment of temple floors, due mainly to their aesthetic and symmetric qualities. Specific yantras are traditionally associated with specific deities and/or certain types of energies used for accomplishment of certain tasks or vows that may be either materialistic or spiritual in nature. They become a prime tool in certain sadhanas performed by the sadhaka, the spiritual seeker. Yantras hold great importance in Hinduism, Jainism, and Buddhism. Representations of the yantra in India have been considered to date back to 11,000–10,000 BCE. The Baghor stone, found in an Upper Paleolithic context in the Son River Valley, is considered the ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seal Of Solomon
The Seal of Solomon or Ring of Solomon (, '; , ') is the legendary Seal (emblem), signet ring attributed to king Solomon in medieval mystical traditions, from which it developed in parallel within Jewish mysticism, Sufism, Islamic mysticism and Western esotericism, Western occultism. It is often depicted in the shape of either a hexagram or a pentagram. In mystic Jewish and Islamic lore, the ring is variously described as having given Solomon the power to command the supernatural, including ' and ', and also the ability to speak with animals. Due to the proverbial wisdom of Solomon, it came to be seen as an amulet or talisman, or a symbol or character in Medieval European magic, medieval magic and Renaissance magic, occultism, and alchemy. The seal is the predecessor to the Star of David, a Jewish symbol, and in modern vexillology, it features on the Flag of Israel. The pentagram on the Flag of Morocco also represents the seal. The Seal of Solomon was also depicted on the Flag o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Star Figure
In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but they can also include disconnected sets of edges, called a compound polygon. For example, a regular pentagram, , has 5 sides, and the regular hexagram, or 2, has 6 sides divided into two triangles. A regular polygram can either be in a set of regular star polygons (for gcd(''p'',''q'') = 1, ''q'' > 1) or in a set of regular polygon compounds (if gcd(''p'',''q'') > 1). Etymology The polygram names combine a numeral prefix, such as ''penta-'', with the Greek suffix '' -gram'' (in this case generating the word ''pentagram''). The prefix is normally a Greek cardinal, but synonyms using other prefixes exist. The ''-gram'' suffix derives from ''γραμμῆς'' (''grammos'') meaning a line. Generalized regular polygons A regular polygram, as a general regular polygon, is denoted by its Schläfli symbol , where ''p'' and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentagram
A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon. Drawing a circle around the five points creates a similar symbol referred to as the pentacle, which is used widely by Wiccans and in paganism, or as a sign of life and connections. The word ''pentagram'' comes from the Greek language, Greek word πεντάγραμμον (''pentagrammon''), from πέντε (''pente''), "five" + γραμμή (''grammē''), "line". The word pentagram refers to just the star and the word pentacle refers to the star within a circle, although there is some overlap in usage. The word ''pentalpha'' is a 17th-century revival of a post-classical Greek name of the shape. History Early history Early pentagrams have been found on Sumerian pottery from Ur c. 3500 Common Era, BCE, and the five-pointed star was at various times the symbol of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Hexagon As Intersection Of Two Triangles
Regular may refer to: Arts, entertainment, and media Music * "Regular" (Badfinger song) * Regular tunings of stringed instruments, tunings with equal intervals between the paired notes of successive open strings Other uses * Regular character, a main character who appears more frequently and/or prominently than a recurring character * Regular division of the plane, a series of drawings by the Dutch artist M. C. Escher which began in 1936 Language * Regular inflection, the formation of derived forms such as plurals in ways that are typical for the language ** Regular verb * Regular script, the newest of the Chinese script styles Mathematics Algebra and number theory * Regular category, a kind of category that has similarities to both Abelian categories and to the category of sets * Regular chains in computer algebra * Regular element (other), certain kinds of elements of an algebraic structure * Regular extension of fields * Regular ideal (multiple definitions) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cube
A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It is a type of parallelepiped, with pairs of parallel opposite faces, and more specifically a rhombohedron, with congruent edges, and a rectangular cuboid, with right angles between pairs of intersecting faces and pairs of intersecting edges. It is an example of many classes of polyhedra: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron. The cube can be represented in many ways, one of which is the graph known as the cubical graph. It can be constructed by using the Cartesian product of graphs. The cube is the three-dimensional hypercube, a family of polytopes also including the two-dimensional square and four-dimensional tesseract. A cube with 1, unit s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mandala
A mandala (, ) is a geometric configuration of symbols. In various spiritual traditions, mandalas may be employed for focusing attention of practitioners and adepts, as a spiritual guidance tool, for establishing a sacred space and as an aid to meditation and trance induction. In the Eastern religions of Hinduism, Buddhism, Jainism and Shinto it is used as a map representing deities, or especially in the case of Shinto, paradises, kami or actual shrines. Hinduism In Hinduism, a basic mandala, also called a '' yantra'', takes the form of a square with four gates containing a circle with a centre point. Each gate is in the general shape of a T. Mandalas often have radial balance. A '' yantra'' is similar to a mandala, usually smaller and using a more limited colour palette. It may be a two- or three-dimensional geometric composition used in '' sadhanas'', puja or meditative rituals, and may incorporate a mantra into its design. It is considered to represent the abode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
India
India, officially the Republic of India, is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area; the List of countries by population (United Nations), most populous country since 2023; and, since its independence in 1947, the world's most populous democracy. Bounded by the Indian Ocean on the south, the Arabian Sea on the southwest, and the Bay of Bengal on the southeast, it shares land borders with Pakistan to the west; China, Nepal, and Bhutan to the north; and Bangladesh and Myanmar to the east. In the Indian Ocean, India is near Sri Lanka and the Maldives; its Andaman and Nicobar Islands share a maritime border with Thailand, Myanmar, and Indonesia. Modern humans arrived on the Indian subcontinent from Africa no later than 55,000 years ago., "Y-Chromosome and Mt-DNA data support the colonization of South Asia by modern humans originating in Africa. ... Coalescence dates for most non-European populations averag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nara-narayana
Naranarayana (), also rendered Nara-Narayana, is a Hindu duo of sage-brothers. Generally regarded to be the partial-incarnation (aṃśa-avatara) of the preserver deity, Vishnu, on earth, Nara-Narayana are described to be the sons of Dharma and Ahimsa. The Hindu scripture ''Mahabharata'' identifies the prince Arjuna with Nara, and the deity Krishna with Narayana. The legend of Nara-Narayana is also told in the scripture ''Bhagavata Purana''. Hindus believe that the pair dwells at Badrinath, where their most important temple stands. Etymology The name "Nara-Narayana" can be broken into two Sanskrit terms, ''Nara'' and ''Narayana''. Nara means 'male being', and Narayana refers to the name of the deity Vishnu. Monier-Williams dictionary says Nara is "the primeval Man or eternal Spirit pervading the universe always associated with Narayana, "son of the primeval man". In epic poetry, they are the sons of Dharma by Murti or Ahimsa, and emanations of Vishnu, Arjuna being identi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
