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Elongated Hexagonal Bipyramid
In geometry, the elongated hexagonal bipyramid is constructed by elongating a hexagonal bipyramid (by inserting a hexagonal prism between its congruent halves). Related polyhedra This polyhedron is in the family of elongated bipyramids, of which the first three can be Johnson solids: J14, J15, and J16. The hexagonal form can be constructed by all regular faces but is not a ''Johnson solid'' because 6 equilateral triangles would form six co-planar faces (in a regular hexagon). Uses * A quartz crystal is an example of an elongated hexagonal bipyramid. Because it has 18 faces, it can be called an octadecahedron. Other chemicals also have this shape. * The ''edge-first orthogonal projection'' of a 24-cell is an elongated hexagonal bipyramid. * Used as the shape of Fruit Gushers candy. * Used as a physical manifestation for assisting various branches of three-dimensional graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elongated Bipyramid
In geometry, the elongated bipyramids are an infinite set of polyhedra, constructed by elongating an bipyramid (by inserting an prism between its congruent halves). There are three ''elongated bipyramids'' that are Johnson solids: * Elongated triangular bipyramid (), * Elongated square bipyramid (), and * Elongated pentagonal bipyramid (). Higher forms can be constructed with isosceles triangles. Forms Applications Elongated bipyramids are sometimes used as dice, especially to make dice with atypical side count, such as 5 or 7. Such a die has numbers written on the square faces, which are usually heightened into rectangles for convenience in rolling. Whichever number comes face-up when the die is rolled is the side that is to be read. See also * Gyroelongated bipyramid * Gyroelongated pyramid * Elongated pyramid * Diminished trapezohedron In geometry, a diminished trapezohedron is a polyhedron in an infinite set of polyhedra, constructed by removing one of the pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elongated Triangular Bipyramid
In geometry, the elongated triangular bipyramid (or dipyramid) or triakis triangular prism a polyhedron constructed from a triangular prism by attaching two tetrahedrons to its bases. It is an example of Johnson solid. Construction The elongated triangular bipyramid is constructed from a triangular prism by attaching two tetrahedrons onto its bases, a process known as the elongation. These tetrahedrons cover the triangular faces so that the resulting polyhedron has nine faces (six of them are equilateral triangles and three of them are squares), fifteen edges, and eight vertices. A convex polyhedron in which all of the faces are regular polygons is the Johnson solid. The elongated bipyramid is one of them, enumerated as the fourteenth Johnson solid J_ . Properties The surface area of an elongated triangular bipyramid A is the sum of all polygonal face's area: six equilateral triangles and three squares. The volume of an elongated triangular bipyramid V can be ascertaine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fruit Gushers
Fruit Gushers (also simply Gushers) are a Betty Crocker-branded fruit snack introduced in 1991. They are soft and chewy with a fruity-juice center. History Fruit Gushers (sometimes simply "Gushers") were introduced in 1991 as a Betty Crocker fruit snack. Each box of Fruit Gushers was list priced at and contained six pouches of Gushers, each of which had nine individual pieces for per pouch. Composition Strawberry-flavored Fruit Gushers are composed of sugar, dried corn syrup, corn syrup, modified corn starch, fructose, pear concentrate, and grape juice concentrate. Targeted at children, they were acorn-shaped with a soft "licorice-like" exterior and a liquid inside, included "strawberries and pear puree concentrate", and came in two flavors: "Strawberry Splash" and "Gushin' Grape". In 2003, one serving of any Fruit Gushers variety was one package with 90 calories, zero protein, of fat, and of carbohydrates. In 2018, 90 calories worth of Strawberry Fruit Gushers weigh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
24-cell
In four-dimensional space, four-dimensional geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is also called C24, or the icositetrachoron, octaplex (short for "octahedral complex"), icosatetrahedroid, Octacube (sculpture), octacube, hyper-diamond or polyoctahedron, being constructed of Octahedron, octahedral Cell (geometry), cells. The boundary of the 24-cell is composed of 24 octahedron, octahedral cells with six meeting at each vertex, and three at each edge. Together they have 96 triangular faces, 96 edges, and 24 vertices. The vertex figure is a cube. The 24-cell is self-dual polyhedron, self-dual. The 24-cell and the tesseract are the only convex regular 4-polytopes in which the edge length equals the radius. The 24-cell does not have a regular analogue in three dimensions or any other number of dimensions, either below or above. It is the only one of the six convex regular 4-polytopes which is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octadecahedron
In geometry, an octadecahedron (or octakaidecahedron) is a polyhedron with 18 face (geometry), faces. No octadecahedron is regular polyhedron, regular; hence, the name does not commonly refer to one specific polyhedron. In chemistry, "''the'' octadecahedron" commonly refers to a specific structure with C2v symmetry, the edge-contracted icosahedron, formed from a regular icosahedron with one edge Edge contraction, contracted. It is the shape of the closo-boranate ion [boron, B11hydrogen, H11]2−. Convex There are 107,854,282,197,058 topologically distinct ''convex'' octadecahedra, excluding mirror images, having at least 11 vertices. (Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.) Examples The most familiar octadecahedra are the heptadecagonal pyramid (geometry), pyramid ... [...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] |
Elongated Pentagonal Bipyramid
In geometry, the elongated pentagonal bipyramid is a polyhedron constructed by attaching two pentagonal pyramids onto the base of a pentagonal prism. It is an example of Johnson solid. Construction The elongated pentagonal bipyramid is constructed from a pentagonal prism by attaching two pentagonal pyramids onto its bases, a process called elongation. These pyramids cover the pentagonal faces so that the resulting polyhedron ten equilateral triangles and five squares. A convex polyhedron in which all of the faces are regular polygons is the Johnson solid. The elongated pentagonal bipyramid is among them, enumerated as the sixteenth Johnson solid J_ . Properties The surface area of an elongated pentagonal bipyramid A is the sum of all polygonal faces' area: ten equilateral triangles, and five squares. Its volume V can be ascertained by dissecting it into two pentagonal pyramids and one regular pentagonal prism and then adding its volume. Given an elongated pentagonal bip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elongated Square Bipyramid
In geometry, the elongated square bipyramid (or elongated octahedron) is the polyhedron constructed by attaching two Equilateral square pyramid, equilateral square pyramids onto a cube (geometry), cube's faces that are opposite each other. It can also be seen as 4 lunes (squares with triangles on opposite sides) linked together with squares to squares and triangles to triangles. It is also been named the pencil cube or 12-faced pencil cube due to its shape. A zircon crystal is an example of an elongated square bipyramid. Construction The elongated square bipyramid is constructed by attaching two Equilateral square pyramid, equilateral square pyramids onto the faces of a Cube (geometry), cube that are opposite each other, a process known as Elongation (geometry), elongation. This construction involves the removal of those two squares and replacing them with those pyramids, resulting in eight Equilateral triangle, equilateral triangles and four squares as their faces.. A convex p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johnson Solid
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two Solid geometry, solids with such a property: the first solids are the Pyramid (geometry), pyramids, Cupola (geometry), cupolas, and a Rotunda (geometry), rotunda; some of the solids may be constructed by attaching with those previous solids, whereas others may not. Definition and background A Johnson solid is a convex polyhedron whose faces are all regular polygons. The convex polyhedron means as bounded intersections of finitely many Half-space (geometry), half-spaces, or as the convex hull of finitely many points. Although there is no restriction that any given regular polygon cannot be a face of a Johnson solid, some authors required that Johnson solids are not Uniform polyhedron, uniform. This means that a Johnson solid is not a Platonic solid, Arc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the ''base'', in which case the opposite vertex is called the ''apex''; the shortest segment between the base and apex is the ''height''. The area of a triangle equals one-half the product of height and base length. In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points that do not all lie on the same straight line determine a unique triangle situated w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elongated Bipyramid
In geometry, the elongated bipyramids are an infinite set of polyhedra, constructed by elongating an bipyramid (by inserting an prism between its congruent halves). There are three ''elongated bipyramids'' that are Johnson solids: * Elongated triangular bipyramid (), * Elongated square bipyramid (), and * Elongated pentagonal bipyramid (). Higher forms can be constructed with isosceles triangles. Forms Applications Elongated bipyramids are sometimes used as dice, especially to make dice with atypical side count, such as 5 or 7. Such a die has numbers written on the square faces, which are usually heightened into rectangles for convenience in rolling. Whichever number comes face-up when the die is rolled is the side that is to be read. See also * Gyroelongated bipyramid * Gyroelongated pyramid * Elongated pyramid * Diminished trapezohedron In geometry, a diminished trapezohedron is a polyhedron in an infinite set of polyhedra, constructed by removing one of the pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagonal Prism
In geometry, the hexagonal prism is a Prism (geometry), prism with hexagonal base. Prisms are polyhedrons; this polyhedron has 8 face (geometry), faces, 18 Edge (geometry), edges, and 12 vertex (geometry), vertices.. As a semiregular polyhedron If faces are all regular, the hexagonal prism is a semiregular polyhedron—more generally, a uniform polyhedron—and the fourth in an infinite set of prisms formed by square sides and two regular polygon caps. It can be seen as a truncation (geometry), truncated hosohedron, hexagonal hosohedron, represented by Schläfli symbol t. Alternately it can be seen as the Cartesian product of a regular hexagon and a line segment, and represented by the product ×. The dual polyhedron, dual of a hexagonal prism is a hexagonal bipyramid. The symmetry group of a right hexagonal prism is prismatic symmetry D_ of order 24, consisting of rotation around an axis passing through the regular hexagon bases' center, and reflection across a hori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
