geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, a bicone or dicone (from la, bi-, and

Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...

: ''di-'', both meaning "two") is the three-dimensional

surface of revolution A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) around an axis of rotation. Examples of surfaces of revolution generated by a straight line are cylindrical and conical surfaces depending on ...

of a

rhombus In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The ...

around one of its

axes of symmetry In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D ther ...

. Equivalently, a bicone is the surface created by joining two

congruent Congruence may refer to: Mathematics * Congruence (geometry), being the same size and shape * Congruence or congruence relation, in abstract algebra, an equivalence relation on an algebraic structure that is compatible with the structure * In mod ...

, right, circular

cones A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines conn ...

at their bases. A bicone has

circular symmetry In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself. Rotational circular symmetry is isomorphic with the circle group in the complex plane, or the ...

and orthogonal

bilateral symmetry Symmetry in biology refers to the symmetry observed in organisms, including plants, animals, fungi, and bacteria. External symmetry can be easily seen by just looking at an organism. For example, take the face of a human being which has a pla ...

Geometry

For a circular bicone with radius ''R'' and height center-to-top ''H'', the formula for volume becomes :

V = \frac \pi R^2 H.

For a right circular cone, the surface area is :

SA =2\pi R S\,

where

S = \sqrt

is the

slant height Slant can refer to: Bias *Bias or other non- objectivity in journalism, politics, academia or other fields Technical * Slant range, in telecommunications, the line-of-sight distance between two points which are not at the same level *Slant d ...

References

External links

* Elementary geometry Surfaces {{Elementary-geometry-stub

Geometry

See also

References

External links