"B Sides and C Sides B Sides and C Sides is a compilation album by the American punk rock band Rancid. It was first released online on December 11, 2007, followed by a standard release on January 15, 2008. It contains a number of B-sides and rare songs as well as compilation or soundtrack appearances plus 4 previously unreleased songs. The set spans from 1992 to 2004, therefore it doesn't include any songs recorded with current drummer Branden Steineckert. ""B Sides and C Sides"" is also notable as being the band's first release since their hiatus in 2004, along with"
"following: Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides. Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals. It follows that any rhombus has the following properties: The first property implies that every rhombus is a parallelogram. A rhombus therefore has all of the properties of a parallelogram: for example, opposite sides are parallel; adjacent angles are supplementary; the two diagonals bisect one another; any line through the midpoint bisects the area; and the sum of the squares of the sides equals the sum of"
"a kite. A rhombus with right angles is a square. The word ""rhombus"" comes from Greek (""rhombos""), meaning something that spins, which derives from the verb ῥέμβω (""rhembō""), meaning ""to turn round and round."" The word was used both by Euclid and Archimedes, who used the term ""solid rhombus"" for two right circular cones sharing a common base. The surface we refer to as ""rhombus"" today is a cross section of this solid rhombus through the apex of each of the two cones. A simple (non-self-intersecting) quadrilateral is a rhombus if and only if it is any one of the"
"Golden rhombus In geometry, a golden rhombus is a rhombus whose diagonals are in the ratio formula_1, where formula_2 is the golden ratio. The internal angles of the rhombus are The edge length of the golden rhombus with short diagonal formula_5 is A golden rhombus with unit edge length has diagonal lengths The Area is Several notable polyhedra have golden rhombi as their faces. They include the two golden rhombohedra (with six faces each), the Bilinski dodecahedron (with 12 faces), the rhombic icosahedron (with 20 faces), the rhombic triacontahedron (with 30 faces), and the nonconvex rhombic hexecontahedron (with 60 faces)."
"The first five of these are the only convex polyhedra with golden rhomb faces, but there exist infinitely many nonconvex polyhedra having this shape for all of its faces. Golden rhombus In geometry, a golden rhombus is a rhombus whose diagonals are in the ratio formula_1, where formula_2 is the golden ratio. The internal angles of the rhombus are The edge length of the golden rhombus with short diagonal formula_5 is A golden rhombus with unit edge length has diagonal lengths The Area is Several notable polyhedra have golden rhombi as their faces. They include the two golden rhombohedra (with"
"Rhomboid Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled. A parallelogram with sides of equal length (equilateral) is a rhombus but not a rhomboid. A parallelogram with right angled corners is a rectangle but not a rhomboid. The term ""rhomboid"" is now more often used for a rhombohedron or a more general parallelepiped, a solid figure with six faces in which each face is a parallelogram and pairs of opposite faces lie in parallel planes. Some crystals are formed in three-dimensional rhomboids. This solid is also"
"a rectangle: The sides of a rhombus centered at the origin, with diagonals each falling on an axis, consist of all points (""x, y"") satisfying The vertices are at formula_11 and formula_12 This is a special case of the superellipse, with exponent 1. A rhombohedron is a three-dimensional figure like a cube, except that its six faces are rhombi instead of squares. The rhombic dodecahedron is a convex polyhedron with 12 congruent rhombi as its faces. The rhombic triacontahedron is a convex polyhedron with 30 golden rhombi (rhombi whose diagonals are in the golden ratio) as its faces. The great"
"the Penrose tiling which uses two kinds of rhombi with 36° and 72° acute angles aperiodically. When more than one type of rhombus is allowed, additional tilings are possible, including some that are topologically equivalent to the rhombille tiling but with lower symmetry. Rhombille tiling In geometry, the rhombille tiling, also known as tumbling blocks, reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called diamonds. Sets of three rhombi meet at their 120° angles and"
"Rhombic enneacontahedron A rhombic enneacontahedron (plural: rhombic enneacontahedra) is a polyhedron composed of 90 rhombic faces; with three, five, or six rhombi meeting at each vertex. It has 60 broad rhombi and 30 slim. The rhombic enneacontahedron is a zonohedron with a superficial resemblance to the rhombic triacontahedron. It can also be seen as a nonuniform truncated icosahedron with pyramids augmented to the pentagonal and hexagonal faces with heights adjusted until the dihedral angles are zero, and the two pyramid type side edges are equal length. This construction is expressed in the Conway polyhedron notation ""jtI"" with join operator ""j""."
"Rhombille tiling In geometry, the rhombille tiling, also known as tumbling blocks, reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called diamonds. Sets of three rhombi meet at their 120° angles and sets of six rhombi meet at their 60° angles. The rhombille tiling can be seen as a subdivision of a hexagonal tiling with each hexagon divided into three rhombi meeting at the center point of the hexagon. This subdivision represents a regular compound"
"Rhombic triacontahedron In geometry, the rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid, and the dual polyhedron of the icosidodecahedron. It is a zonohedron. The ratio of the long diagonal to the short diagonal of each face is exactly equal to the golden ratio, ""φ"", so that the acute angles on each face measure , or approximately 63.43°. A rhombus so obtained is called a ""golden rhombus"". Being the dual"
"Rhombic icosahedron A rhombic icosahedron is a polyhedron shaped like an oblate sphere. It is composed of 20 rhombic faces, of which three, four, or five meet at each vertex. It has 10 faces on the axis of symmetry with 10 rhombi following the equator. It has D, [2,10], (2*5) symmetry, order 20. Even though all the faces are congruent, the rhombic icosahedron is not face-transitive, since one may distinguish whether a particular face is near the equator or a pole by examining the types of vertices surrounding that face. The rhombic icosahedron is a zonohedron that is dual to"
"1 + = ) known as a Kepler triangle. A golden rhombus is a rhombus whose diagonals are in the golden ratio. The rhombic triacontahedron is a convex polytope that has a very special property: all of its faces are golden rhombi. In the rhombic triacontahedron the dihedral angle between any two adjacent rhombi is 144°, which is twice the isosceles angle of a golden triangle and four times its most acute angle. A square pyramid in which the apothem (slant height along the bisector of a face) is equal to φ times the semi-base (half the base width) is"
"Rhombic hectotriadiohedron In geometry, a rhombic hectotriadiohedron, rhombhectotriadiohedron or rhombic 132-hedron is a polyhedron composed of 132 rhombic faces. Rhombic faces have 5 positions within octahedral symmetry. There are two topological types, with the same number of elements, the same symmetry, but having a somewhat different arrangement of rhombic faces. The type T has 8 rhombi meeting at the center positions of a cube's 6 faces. 3 meet at the 8 corners of a cube. 12 are positioned along the 12 edges of a cube, and 4 more surround each of 12 edges of a cube. It is a 12-zone"
"Rhombohedron In geometry, a rhombohedron is a three-dimensional figure like a cube, except that its faces are not squares but rhombi. It is a special case of a parallelepiped where all edges are the same length. It can be used to define the rhombohedral lattice system, a honeycomb with rhombohedral cells. In general the ""rhombohedron"" can have three types of rhombic faces in congruent opposite pairs, ""C"" symmetry, order 2. Four points forming non-adjacent vertices of a rhombohedron necessarily form the four vertices of an orthocentric tetrahedron, and all orthocentric tetrahedra can be formed in this way. The rhombohedral lattice"
"Without the equal edge constraint, the wide rhombi are kites if limited only by the icosahedral symmetry. The sixty broad rhombic faces in the rhombic enneacontahedron are identical to those in the rhombic dodecahedron, with diagonals in a ratio of 1 to the square root of 2. The face angles of these rhombi are approximately 70.528° and 109.471°. The thirty slim rhombic faces have face vertex angles of 41.810° and 138.189°; the diagonals are in ratio of 1 to φ. It is also called a rhombic enenicontahedron in Lloyd Kahn's ""Domebook 2"". The optimal packing fraction of rhombic enneacontahedra is"
"system has rhombohedral cells, with 3 pairs of unique rhombic faces: For a unit rhombohedron (side length = 1) whose rhombic acute angle is θ and has one vertex is at the origin (0, 0, 0) with one edge lying along the x-axis the three vectors are The other coordinates can be obtained from vector addition of the 3 direction vectors so that e + e, e + e, e + e, and e + e + e The volume of the rhombohedron whose side length is ""'a""' is a simplification of the volume of a parallelepiped and is given"
"around 180 degrees and then turned upside down, the result is as shown in Figure 6. Figure 6 shows three lobes seen sideways. Between each pair of lobes there is a locus of double points corresponding to a coordinate axis. The three loci intersect at a triple point at the origin. The fourth lobe is hidden and points in the direction directly opposite from the viewer. The Roman surface shown at the top of this article also has three lobes in sideways view. The Roman surface is non-orientable, i.e. one-sided. This is not quite obvious. To see this, look again"
"describe a geometric rhomboid (e.g. the rhomboid muscles) or a bilaterally-symmetrical kite-shaped or diamond-shaped outline, as in leaves or cephalopod fins. In a type of arthritis called pseudogout, crystals of calcium pyrophosphate dihydrate accumulate in the joint, causing inflammation. Aspiration of the joint fluid reveals rhomboid-shaped crystals under a microscope. Rhomboid Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled. A parallelogram with sides of equal length (equilateral) is a rhombus but not a rhomboid. A parallelogram with right angled corners is a rectangle but not a"
"with 60° internal angles. An equilateral quadrilateral is called a rhombus, an isotoxal polygon described by an angle α. It includes the square as a special case. A convex equilateral pentagon can be described by two angles α and β, which together determine the other angles. Concave equilateral pentagons exist, as do concave equilateral polygons with any larger number of sides. An equilateral polygon which is cyclic (its vertices are on a circle) is a regular polygon (a polygon that is both equilateral and equiangular). A tangential polygon (one that has an incircle tangent to all its sides) is equilateral"
"Rhumb line In navigation, a rhumb line, rhumb, or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true or magnetic north. The effect of following a rhumb line course on the surface of a globe was first discussed by the Portuguese mathematician Pedro Nunes in 1537, in his ""Treatise in Defense of the Marine Chart"", with further mathematical development by Thomas Harriot in the 1590s. A rhumb line can be contrasted with a great circle, which is the path of shortest distance between two"
"The five cases correspond to the triangle being equilateral, right isosceles, right, isosceles, and scalene. In a rhombic lattice, the shortest distance may either be a diagonal or a side of the rhombus, i.e., the line segment connecting the first two points may or may not be one of the equal sides of the isosceles triangle. This depends on the smaller angle of the rhombus being less than 60° or between 60° and 90°. The general case is known as a period lattice. If the vectors p and q generate the lattice, instead of p and q we can also"
"sometimes called a rhombic prism. The term occurs frequently in science terminology referring to both its two- and three-dimensional meaning. Euclid introduced the term in his ""Elements"" in Book I, Definition 22, Euclid never used the definition of rhomboid again and introduced the word parallelogram in Proposition 31 of Book I; """"In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas."""" Heath suggests that rhomboid was an older term already in use. The rhomboid has no line of symmetry, but it has rotational symmetry of order 2. In biology, rhomboid may"
"for all parallelograms, the area ""K"" of a rhombus is the product of its base and its height (""h""). The base is simply any side length ""a"": The area can also be expressed as the base squared times the sine of any angle: or in terms of the height and a vertex angle: or as half the product of the diagonals ""p"", ""q"": or as the semiperimeter times the radius of the circle inscribed in the rhombus (inradius): Another way, in common with parallelograms, is to consider two adjacent sides as vectors, forming a bivector, so the area is the"
"rhombus, or triangle is rep-4. The sphinx hexiamond (illustrated above) is rep-4 and rep-9, and is one of few known self-replicating pentagons. The Gosper island is rep-7. The Koch snowflake is irrep-7: six small snowflakes of the same size, together with another snowflake with three times the area of the smaller ones, can combine to form a single larger snowflake. A right triangle with side lengths in the ratio 1:2 is rep-5, and its rep-5 dissection forms the basis of the aperiodic pinwheel tiling. By Pythagoras' theorem, the hypotenuse, or sloping side of the rep-5 triangle, has a length of"
"that it starts sliding down towards the ""x = 0"" axis. As soon as the ant crosses this axis it will find itself ""inside"" the Northern lobe, standing right side up. Now let the ant walk towards the North. It will climb up the wall, then along the ""roof"" of the Northern lobe. The ant is back on the third hyperbolic paraboloid, but this time under it and standing upside-down. (Compare with Klein bottle.) The Roman surface has four ""lobes"". The boundaries of each lobe are a set of three lines of double points. Between each pair of lobes there"
"an irregular-faced pentagonal gyrobicupola. It has 5 sets of 8 parallel edges, described as 8 belts. The rhombic icosahedron forms the convex hull of the vertex-first projection of a 5-cube to 3 dimensions. The 32 vertices of a 5-cube map into 22 exterior vertices of the rhombic icosahedron, with the remaining 10 interior vertices forming a pentagonal antiprism. This is the same way one can obtain a Bilinski dodecahedron from a 4-cube and a rhombic triacontahedron from a 6-cube. The rhombic icosahedron can be derived from the rhombic triacontahedron by removing 10 middle faces. Rhombic icosahedron A rhombic icosahedron is"
"rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron with 30 intersecting rhombic faces. The rhombic hexecontahedron is a stellation of the rhombic triacontahedron. It is nonconvex with 60 golden rhombic faces with icosahedral symmetry. The rhombic enneacontahedron is a polyhedron composed of 90 rhombic faces, with three, five, or six rhombi meeting at each vertex. It has 60 broad rhombi and 30 slim ones. The trapezo-rhombic dodecahedron is a convex polyhedron with 6 rhombic and 6 trapezoidal faces. The rhombic icosahedron is a polyhedron composed of 20 rhombic faces, of which three, four, or five meet at each vertex. It"
"Humerus The humerus (, plural: ""humeri"") is a long bone in the arm that runs from the shoulder to the elbow. It connects the scapula and the two bones of the lower arm, the radius and ulna, and consists of three sections. The humeral upper extremity consists of a rounded head, a narrow neck, and two short processes (tubercles, sometimes called tuberosities). The body is cylindrical in its upper portion, and more prismatic below. The lower extremity consists of 2 epicondyles, 2 processes (trochlea & capitulum), and 3 fossae (radial fossa, coronoid fossa, and olecranon fossa). As well as its"
"pentagons around the sides which alternate upwards and downwards. This form has a hexagonal cross-section and identical copies can be connected as a partial hexagonal honeycomb, but all vertices will not match. The ""rhombic dodecahedron"" is a zonohedron with twelve rhombic faces and octahedral symmetry. It is dual to the quasiregular cuboctahedron (an Archimedean solid) and occurs in nature as a crystal form. The rhombic dodecahedron packs together to fill space. The ""rhombic dodecahedron"" can be seen as a degenerate pyritohedron where the 6 special edges have been reduced to zero length, reducing the pentagons into rhombic faces. The rhombic"
"the latter case the quadrilateral is a tangential quadrilateral. Each diagonal of a rhombus bisects opposite angles. The excenter of an ex-tangential quadrilateral lies at the intersection of six angle bisectors. These are the internal angle bisectors at two opposite vertex angles, the external angle bisectors (supplementary angle bisectors) at the other two vertex angles, and the external angle bisectors at the angles formed where the extensions of opposite sides intersect. The tangent to a parabola at any point bisects the angle between the line joining the point to the focus and the line from the point and perpendicular to"
"polyhedra. Every golden rhombic face has a face center, a vertex, and two edge centers of the original dodecahedron, with the edge centers forming the short diagonal. Each edge center is connected to two vertices and two face centers. Each face center is connected to five edge centers, and each vertex is connected to three edge centers. The ""rhombic hexecontahedron"" is one of 227 self-supporting stellations of the rhombic triacontahedron. Its stellation diagram looks like this, with the original rhombic triacontahedron faces as the central rhombus. The great rhombic triacontahedron contains the 30 larger intersecting rhombic faces: The Rhombic hexacontahedron"
"four sides equal to ; (we have a right triangle whose hypotenuse is and the side opposite to the angle is ). The pale lines correspond to the small diagonal of the rhombus. As the diagonals are the bisectors of the neighbouring sides, we can see that the pale line makes an angle equal to with the perpendicular of each pattern's line. Additionally, the spacing between two pale lines is , half of the long diagonal. The long diagonal is the hypotenuse of a right triangle and the sides of the right angle are and . The Pythagorean theorem gives:"