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**Through and through** describes a situation where an object, real or imaginary, passes completely through another object, also real or imaginary. The phrase has several common uses:

Through and through is used in forensics to describe a bullet that has passed through a body, leaving both entry and exit wounds Example..

An image may be through and through in the following cases:

- ink or paint has penetrated to the other side
- inlaying with another material, stained glass, patchwork, woodwork, linoleum, marble, etc.
- carving out (e.g. wood carving), cutting out, perforation: this may concern the outside shape, shaped holes, and patterns of holes (e.g. in a punched card; also a passport may have its number perforated in the pages, to make forgery more difficult).
- embroidery etc.

Through and through images are more durable; they do not easily wear off.

In the case that the image can be viewed from the other side, we see the mirror image, just like in the case of a transparent image, such as a drawing on a transparent sheet.

A sheet with a through and through image is achiral. We can distinguish two cases:

- the sheet surface with the image has no axis of symmetry parallel to the axis of rotation – the two sides are the same (e.g. U on a page rotated L–R)
- the sheet surface with the image has an axis of symmetry parallel to the axis of rotation – the two sides are different (e.g. C on a page rotated L–R)

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**Precession** is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called *nutation*. In physics, there are two types of precession: torque-free and torque-induced.

A **sphere** is a geometrical object in three-dimensional space that is the surface of a ball.

**2D computer graphics** is the computer-based generation of digital images—mostly from two-dimensional models and by techniques specific to them. The word may stand for the branch of computer science that comprises such techniques or for the models themselves.

A **rotation** is a circular movement of an object around a center of rotation. A three-dimensional object can always be rotated about an infinite number of imaginary lines called *rotation axes*. If the axis passes through the body's center of mass, the body is said to rotate upon itself, or spin. A rotation around an external point, e.g. the planet Earth around the Sun, is called a *revolution* or *orbital revolution*, typically when it is produced by gravity. The axis is called a **pole**.

An **equatorial bulge** is a difference between the equatorial and polar diameters of a planet, due to the centrifugal force exerted by the rotation about the body's axis. A rotating body tends to form an oblate spheroid rather than a sphere.

In geometry, a **hyperboloid of revolution**, sometimes called a **circular hyperboloid**, is the surface generated by rotating a hyperbola around one of its principal axes. A **hyperboloid** is the surface obtained from a hyperboloid of revolution by deforming it by means of directional scalings, or more generally, of an affine transformation.

In fluid dynamics, a **vortex** is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado or dust devil.

A **shape** is the form of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture or material type.

In mathematics, the **complex plane** or ** z-plane** is a geometric representation of the complex numbers established by the

A **wallpaper group** is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art, especially in textiles and tiles as well as wallpaper.

In physics, a **rigid body** is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external forces exerted on it. A rigid body is usually considered as a continuous distribution of mass.

The **Kerr metric** or **Kerr geometry** describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find.

In 3D computer graphics, a **lathed** object is a 3D model whose vertex geometry is produced by rotating the points of a spline or other point set around a fixed axis. The lathing may be partial; the amount of rotation is not necessarily a full 360 degrees. The point set providing the initial source data can be thought of as a cross section through the object along a plane containing its axis of radial symmetry.

**Rotational symmetry**, also known as **radial symmetry** in biology, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.

In geometry, to translate a geometric figure is to move it from one place to another without rotating it. A translation "slides" a thing by **a**: *T*_{a}(**p**) = **p** + **a**.

In geometry, a **point group in three dimensions** is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices. O(3) itself is a subgroup of the Euclidean group E(3) of all isometries.

In Gaussian optics, the **cardinal points** consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the **focal points**, the **principal points**, and the **nodal points**. For *ideal* systems, the basic imaging properties such as image size, location, and orientation are completely determined by the locations of the cardinal points; in fact only four points are necessary: the focal points and either the principal or nodal points. The only ideal system that has been achieved in practice is the plane mirror, however the cardinal points are widely used to *approximate* the behavior of real optical systems. Cardinal points provide a way to analytically simplify a system with many components, allowing the imaging characteristics of the system to be approximately determined with simple calculations.

The * Octacube* is a large, stainless steel sculpture displayed in the mathematics department of Pennsylvania State University in State College, PA. The sculpture represents a mathematical object called the 24-cell or "octacube". Because a real 24-cell is four-dimensional, the artwork is actually a projection into the three-dimensional world.

In technical drawing and computer graphics, a **multiview projection** is a technique of illustration by which a standardized series of orthographic two-dimensional pictures are constructed to represent the form of a three-dimensional object. Up to six pictures of an object are produced, with each projection plane parallel to one of the coordinate axes of the object. The views are positioned relative to each other according to either of two schemes: *first-angle* or *third-angle* projection. In each, the appearances of views may be thought of as being *projected* onto planes that form a six-sided box around the object. Although six different sides can be drawn, *usually* three views of a drawing give enough information to make a three-dimensional object. These views are known as *front view*, *top view* and *end view*. Other names for these views include *plan*, *elevation* and *section*.

In astronomy, geography, and related sciences and contexts, a *direction* or *plane* passing by a given point is said to be **vertical** if it contains the local gravity direction at that point. Conversely, a direction or plane is said to be **horizontal** if it is perpendicular to the vertical direction. In general, something that is vertical can be drawn from up to down, such as the y-axis in the Cartesian coordinate system.

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Images, videos and audio are available under their respective licenses.