"ones caused by delivering a blow, are not uncommon. Direct trauma to the bone can also cause fracture. Due to its rarity, standard treatment has not been established. A wide range of treatments are possible, including rest, surgery and casting. The etymology derives from the Greek ""trapezion"" which means ""irregular quadrilateral,"" from ""tra-"" ""four"" and ""peza"" ""foot"" or ""edge."" Literally, ""a little table"" from ""trapeza"" meaning ""table"" and ""-oeides"" ""shaped."" Trapezoid bone The trapezoid bone (lesser multangular bone) is a carpal bone in tetrapods, including humans. It is the smallest bone in the distal row of carpal bones that give"
"Trapezoid In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid () in American and Canadian English but as a trapezium () in English outside North America. The parallel sides are called the ""bases"" of the trapezoid and the other two sides are called the ""legs"" or the lateral sides (if they are not parallel; otherwise there are two pairs of bases). A ""scalene trapezoid"" is a trapezoid with no sides of equal measure, in contrast to the special cases below. The term ""trapezium"" has been in use in English"
"Truncated triangular trapezohedron In geometry, the truncated triangular trapezohedron is the first in an infinite series of truncated trapezohedron polyhedra. It has 6 pentagon and 2 triangle faces. This polyhedron can be constructed by truncating two opposite vertices of a cube, of a trigonal trapezohedron (a convex polyhedron with six congruent rhombus sides, formed by stretching or shrinking a cube along one of its long diagonals), or of a rhombohedron or parallelepiped (less symmetric polyhedra that still have the same combinatorial structure as a cube). In the case of a cube, or of a trigonal trapezohedron where the two truncated"
"subject of several contradictory theories: Truncated triangular trapezohedron In geometry, the truncated triangular trapezohedron is the first in an infinite series of truncated trapezohedron polyhedra. It has 6 pentagon and 2 triangle faces. This polyhedron can be constructed by truncating two opposite vertices of a cube, of a trigonal trapezohedron (a convex polyhedron with six congruent rhombus sides, formed by stretching or shrinking a cube along one of its long diagonals), or of a rhombohedron or parallelepiped (less symmetric polyhedra that still have the same combinatorial structure as a cube). In the case of a cube, or of a trigonal"
"Isosceles trapezoid In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid. Alternatively, it can be defined as a trapezoid in which both legs and both base angles are of the same measure. Note that a non-rectangular parallelogram is not an isosceles trapezoid because of the second condition, or because it has no line of symmetry. In any isosceles trapezoid two opposite sides (the bases) are parallel, and the two other sides (the legs) are of"
"two adjacent acute angles on its longer ""base"" edge, while an obtuse trapezoid has one acute and one obtuse angle on each ""base"". An isosceles trapezoid is a trapezoid where the sides (legs) have the same length, and the base angles have the same measure. It has reflection symmetry. This is possible for acute or right trapezoids. A parallelogram is a trapezoid with two pairs of parallel sides. A parallelogram has central 2-fold rotational symmetry (or point reflection symmetry). It is possible for obtuse or right trapezoids. A tangential trapezoid is a trapezoid that has an incircle. A Saccheri quadrilateral"
"to ""trapezium"" (e.g. Portuguese ""trapézio"", French ""trapèze"", Italian ""trapezio"", Spanish ""trapecio"", German ""Trapez"", Russian ""трапеция"") is used. There is some disagreement whether parallelograms, which have two pairs of parallel sides, should be regarded as trapezoids. Some define a trapezoid as a quadrilateral having ""only"" one pair of parallel sides (the exclusive definition), thereby excluding parallelograms. Others define a trapezoid as a quadrilateral with ""at least"" one pair of parallel sides (the inclusive definition), making the parallelogram a special type of trapezoid. The latter definition is consistent with its uses in higher mathematics such as calculus. The former definition would make"
"and the distance from the perpendicular leg to the diagonal intersection. In morphology, taxonomy and other descriptive disciplines in which a term for such shapes is necessary, terms such as ""trapezoidal"" or ""trapeziform"" commonly are useful in descriptions of particular organs or forms. Trapezoid In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid () in American and Canadian English but as a trapezium () in English outside North America. The parallel sides are called the ""bases"" of the trapezoid and the other two sides are called the ""legs"" or"
"Truncated trapezohedron An ""n""-gonal truncated trapezohedron is a polyhedron formed by a ""n""-gonal trapezohedron with ""n""-gonal pyramids truncated from its two polar axis vertices. If the polar vertices are completely truncated (diminished), a trapezohedron becomes an antiprism. The vertices exist as 4 ""n""-gons in four parallel planes, with alternating orientation in the middle creating the pentagons. The regular dodecahedron is the most common polyhedron in this class, being a platonic solid, with 12 congruent pentagonal faces. A ""truncated trapezohedron"" has all vertices with 3 faces. This means that the dual polyhedra, the set of gyroelongated dipyramids, have all triangular faces."
"Truncated square trapezohedron The square truncated trapezohedron is the second in an infinite series of truncated trapezohedron polyhedra. It has 8 pentagon and 2 square faces. This polyhedron can be constructed by taking a tetragonal trapezohedron and truncating the polar axis vertices. The kite faces of the trapezohedron become pentagons. The vertices exist as 4 squares in four parallel planes, with alternating orientation in the middle creating the pentagons. A ""truncated trapezohedron"" has all valence-3 vertices. This means that the dual polyhedrona gyroelongated square dipyramid has all triangular faces. It represents the dual polyhedron to the Johnson solid, gyroelongated square"
"dipyramid, with specific proportions: Truncated square trapezohedron The square truncated trapezohedron is the second in an infinite series of truncated trapezohedron polyhedra. It has 8 pentagon and 2 square faces. This polyhedron can be constructed by taking a tetragonal trapezohedron and truncating the polar axis vertices. The kite faces of the trapezohedron become pentagons. The vertices exist as 4 squares in four parallel planes, with alternating orientation in the middle creating the pentagons. A ""truncated trapezohedron"" has all valence-3 vertices. This means that the dual polyhedrona gyroelongated square dipyramid has all triangular faces. It represents the dual polyhedron to the"
"on each of the hexagons. Hexagonal bifrustum The hexagonal bifrustum or truncated hexagonal bipyramid is the fourth in an infinite series of bifrustum polyhedra. It has 12 trapezoid and 2 hexagonal faces. This polyhedron can be constructed by taking a hexagonal dipyramid and truncating the polar axis vertices, making it into two end-to-end frustums. Several types of crystal take this shape. It has also been used in the design of 14-sided dice, which may be used to generate randomly chosen playing cards. It also has application in novelty promotional calendars: one month can appear on each of the trapezoids, and"
"equal length (properties shared with the parallelogram). The diagonals are also of equal length. The base angles of an isosceles trapezoid are equal in measure (there are in fact two pairs of equal base angles, where one base angle is the supplementary angle of a base angle at the other base). Rectangles and squares are usually considered to be special cases of isosceles trapezoids though some sources would exclude them. Another special case is a ""3-equal side trapezoid"", sometimes known as a ""trilateral trapezoid"" or a ""trisosceles trapezoid"". They can also be seen dissected from regular polygons of 5 sides"
"Hexagonal bifrustum The hexagonal bifrustum or truncated hexagonal bipyramid is the fourth in an infinite series of bifrustum polyhedra. It has 12 trapezoid and 2 hexagonal faces. This polyhedron can be constructed by taking a hexagonal dipyramid and truncating the polar axis vertices, making it into two end-to-end frustums. Several types of crystal take this shape. It has also been used in the design of 14-sided dice, which may be used to generate randomly chosen playing cards. It also has application in novelty promotional calendars: one month can appear on each of the trapezoids, and an advertising or other message"
"bisecting along a diagonal of the inner square, to give the trapezoid as shown in the diagram. The area of the trapezoid can be calculated to be half the area of the square, that is The inner square is similarly halved, and there are only two triangles so the proof proceeds as above except for a factor of formula_16, which is removed by multiplying by two to give the result. One can arrive at the Pythagorean theorem by studying how changes in a side produce a change in the hypotenuse and employing calculus. The triangle ""ABC"" is a right triangle,"
"divides this segment in the ratio (when taken from the short to the long side) If the angle bisectors to angles ""A"" and ""B"" intersect at ""P"", and the angle bisectors to angles ""C"" and ""D"" intersect at ""Q"", then The term ""trapezoid"" was once defined as a quadrilateral without any parallel sides in Britain and elsewhere. (The Oxford English Dictionary says ""Often called by English writers in the 19th century"".) According to the ""Oxford English Dictionary"", the sense of a figure with no sides parallel is the meaning for which Proclus introduced the term ""trapezoid"". This is retained in"
"Trigonal trapezohedron In geometry, a trigonal trapezohedron or trigonal deltohedron is a three-dimensional figure formed by six congruent rhombi. Six identical rhombic faces can construct two configurations of trigonal trapezohedra. The ""acute"" or ""prolate"" form has three acute angles corners of the rhombic faces meeting at two polar axis vertices. The ""obtuse"" or ""oblate"" or ""flat"" form has three obtuse angle corners of the rhombic faces meeting at the two polar axis vertices. A trigonal trapezohedron is a special case of a rhombohedron. A general rhombohedron allows up to three types of rhombic faces. A trigonal trapezohedron is a special"
"trapezoid ""ABCD"", with bases ""AB"" and ""DC"", are right angles. The incenter lies on the median (also called the midsegment; that is, the segment connecting the midpoints of the legs). The median (midsegment) of a tangential trapezoid equals one fourth of the perimeter of the trapezoid. It also equals half the sum of the bases, as in all trapezoids. If two circles are drawn, each with a diameter coinciding with the legs of a tangential trapezoid, then these two circles are tangent to each other. A right tangential trapezoid is a tangential trapezoid where two adjacent angles are right angles."
"Tetragonal trapezohedron The tetragonal trapezohedron, or deltohedron, is the second in an infinite series of face-uniform polyhedra, which are dual to the antiprisms. It has eight faces, which are congruent kites, and is dual to the square antiprism. This shape has been used as a test case for hexahedral mesh generation, simplifying an earlier test case of Rob Schneider in the form of a square pyramid with its boundary subdivided into 16 quadrilaterals. In this context the tetragonal trapezohedron has also been called the cubical octahedron, quadrilateral octahedron, or octagonal spindle, because it has eight quadrilateral faces and is uniquely"
"may concisely define an isosceles trapezoid as ""a cyclic quadrilateral with equal diagonals"" or as ""a cyclic quadrilateral with a pair of parallel sides"" or as ""a convex quadrilateral with a line of symmetry through the mid-points of opposite sides"". In an isosceles trapezoid, the base angles have the same measure pairwise. In the picture below, angles ∠""ABC"" and ∠""DCB"" are obtuse angles of the same measure, while angles ∠""BAD"" and ∠""CDA"" are acute angles, also of the same measure. Since the lines ""AD"" and ""BC"" are parallel, angles adjacent to opposite bases are supplementary, that is, angles The diagonals"
"10-sided die, if numbered from 0-9, two are commonly used to obtain a percentage roll. Rolling 2 of these are attributed in the results 00-99, where 00 can be also viewed as a 100 as the result in some games. Alone casting a 0-9 ten sided dice, the 0 face is valued at 10. Pentagonal trapezohedron The pentagonal trapezohedron or deltohedron is the third in an infinite series of face-transitive polyhedra which are dual polyhedra to the antiprisms. It has ten faces (i.e., it is a decahedron) which are congruent kites. It can be decomposed into two pentagonal pyramids and"
"kind of parallelepiped, and are the only parallelepipeds with six congruent faces. Since all of the edges must have the same length, every trigonal trapezohedron is also a rhombohedron. It is the simplest of the trapezohedra, an infinite sequence of polyhedra which are dual to the antiprisms. The dual of a ""trigonal trapezohedron"" is a triangular antiprism. A trigonal trapezohedron with square faces is a cube. A lower symmetry variation of the ""trigonal trapezohedron"" has only rotational symmetry, D, and is made from 6 identical irregular quadrilaterals. These quadrilaterals necessarily have two adjacent sides of equal length. A golden rhombohedron"
"trapezoids of size ε. A special trapezoid is an isosceles trapezoid with three equal sides, each longer than the fourth side, inscribed in the curve with a vertex ordering consistent with the clockwise ordering of the curve itself. Its size is the length of the part of the curve that extends around the three equal sides. If there are no such trapezoids (or an even number of them), the limiting argument for general curves can be carried to completion, showing that curves with this property always have an inscribed square. If a Jordan curve inscribed in an annulus whose outer"
"Pentagonal trapezohedron The pentagonal trapezohedron or deltohedron is the third in an infinite series of face-transitive polyhedra which are dual polyhedra to the antiprisms. It has ten faces (i.e., it is a decahedron) which are congruent kites. It can be decomposed into two pentagonal pyramids and a pentagonal antiprism in the middle. It can also be decomposed into two pentagonal pyramids and a dodecahedron in the middle. The pentagonal trapezohedron was patented for use as a gaming die (i.e. ""game apparatus"") in 1906. These dice are used for role-playing games that use percentile-based skills; however, a twenty-sided die can be"
"For example, the icosahedron is the dual of the dodecahedron. <br> Truncated trapezohedron An ""n""-gonal truncated trapezohedron is a polyhedron formed by a ""n""-gonal trapezohedron with ""n""-gonal pyramids truncated from its two polar axis vertices. If the polar vertices are completely truncated (diminished), a trapezohedron becomes an antiprism. The vertices exist as 4 ""n""-gons in four parallel planes, with alternating orientation in the middle creating the pentagons. The regular dodecahedron is the most common polyhedron in this class, being a platonic solid, with 12 congruent pentagonal faces. A ""truncated trapezohedron"" has all vertices with 3 faces. This means that the"
"Truncated triakis tetrahedron The truncated triakis tetrahedron, or more precisely an order-6 truncated triakis tetrahedron, is a convex polyhedron with 16 faces: 4 sets of 3 pentagons arranged in a tetrahedral arrangement, with 4 hexagons in the gaps. It is constructed from taking a triakis tetrahedron by truncating the order-6 vertices. This creates 4 regular hexagon faces, and leaves 12 mirror-symmetric pentagons. A topologically similar equilateral polyhedron can be constructed by using 12 regular pentagons with 4 equilateral but nonplanar hexagons, each vertex with internal angles alternating between 108 and 132 degrees. Topologically, as a near-miss Johnson solid, the four"
"The truncated triangular trapezohedron is another polyhedron which can be formed from cube edge truncation. The ""truncated cube"", is second in a sequence of truncated hypercubes: In the mathematical field of graph theory, a truncated cubical graph is the graph of vertices and edges of the ""truncated cube"", one of the Archimedean solids. It has 24 vertices and 36 edges, and is a cubic Archimedean graph. Truncated cube In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces (6 octagonal and 8 triangular), 36 edges, and 24 vertices. If the truncated cube has"
"Trapezohedron The ""n""-gonal trapezohedron, antidipyramid, antibipyramid or deltohedron is the dual polyhedron of an ""n""-gonal antiprism. With a highest symmetry, its 2""n"" faces are congruent kites (also called trapezia or deltoids). The faces are symmetrically staggered. The ""n""-gon part of the name does not reference the faces here but arrangement of vertices around an axis of symmetry. The dual ""n""-gonal antiprism has two actual ""n""-gon faces. An ""n""-gonal trapezohedron can be dissected into two equal ""n""-gonal pyramids and an ""n""-gonal antiprism. These figures, sometimes called deltohedra, must not be confused with deltahedra, whose faces are equilateral triangles. In texts describing"
"Trapezius The trapezius (or trapezoid) is a large paired surface muscle that extends longitudinally from the occipital bone to the lower thoracic vertebrae of the spine and laterally to the spine of the scapula. It moves the scapula and supports the arm. The trapezius has three functional parts: an upper (descending) part which supports the weight of the arm; a middle region (transverse), which retracts the scapula; and a lower (ascending) part which medially rotates and depresses the scapula. The trapezius muscle resembles a trapezium (trapezoid in American English), or diamond-shaped quadrilateral. The word ""spinotrapezius"" refers to the human trapezius,"
"the circumscribed circle is given by In a rectangle where ""a"" = ""b"" this is simplified to formula_10. Isosceles trapezoid In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid. Alternatively, it can be defined as a trapezoid in which both legs and both base angles are of the same measure. Note that a non-rectangular parallelogram is not an isosceles trapezoid because of the second condition, or because it has no line of symmetry. In any"
"faces ""F"", of vertices ""V"", and of edges ""E"" of any convex polyhedron are related by the formula ""F"" + ""V"" = ""E"" + 2. In the case of a cuboid this gives 6 + 8 = 12 + 2; that is, like a cube, a cuboid has 6 faces, 8 vertices, and 12 edges. Along with the rectangular cuboids, any parallelepiped is a cuboid of this type, as is a square frustum (the shape formed by truncation of the apex of a square pyramid). In a rectangular cuboid, all angles are right angles, and opposite faces of a cuboid"
"of an isosceles trapezoid have the same length; that is, every isosceles trapezoid is an equidiagonal quadrilateral. Moreover, the diagonals divide each other in the same proportions. As pictured, the diagonals ""AC"" and ""BD"" have the same length () and divide each other into segments of the same length ( and ). The ratio in which each diagonal is divided is equal to the ratio of the lengths of the parallel sides that they intersect, that is, The length of each diagonal is, according to Ptolemy's theorem, given by where ""a"" and ""b"" are the lengths of the parallel sides"
"into congruent quadrilaterals with 3 edges lengths. In the limit, one edge of each quadrilateral goes to zero length, and these become bipyramids. If the kites surrounding the two peaks are of different shapes, it can only have C symmetry, order 2""n"". These can be called ""unequal"" or ""asymmetric trapezohedra"". The dual is an ""unequal antiprism"", with the top and bottom polygons of different radii. If it twisted and unequal its symmetry is reduced to cyclic symmetry, C symmetry, order ""n"". A ""n""-trapezohedron has 2""n"" quadrilateral faces, with 2""n""+2 vertices. Two vertices are on the polar axis, and the others"