Examples of Selected Solid Figures and its Definitions
1.CUBE
In geometry, a cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangularparallelepiped and of trigonal trapezohedron. The cube is dual to the octahedron. It has cubical symmetry (also called octahedral symmetry). It is special by being a cuboid and a rhombohedron.
In geometry, a cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangularparallelepiped and of trigonal trapezohedron. The cube is dual to the octahedron. It has cubical symmetry (also called octahedral symmetry). It is special by being a cuboid and a rhombohedron.
2. TRIANGULAR PYRAMID. A triangular pyramid is a pyramid having a triangular base. The tetrahedron is a triangular pyramid having congruent equilateral triangles for each of its faces.
3.CONE.
A cone is an -dimensional geometric shape[clarification needed] that tapers smoothly from a base (usually flat and circular) to a point called the apex or vertex.
A cone is an -dimensional geometric shape[clarification needed] that tapers smoothly from a base (usually flat and circular) to a point called the apex or vertex.
- More precisely, it is the solid figure bounded by a plane base and the surface (called the lateral surface) formed by the locus of all straight line segments joining the apex to the perimeter of the base. The term "cone" sometimes refers just to the surface of this solid figure, or just to the lateral . The axis of a cone is the straight line (if any), passing through the apex, about which the base has a rotational symmetry.
4. CYLINDER.
Cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"[1]) is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder. The surface area and the volume of a cylinder have been known since deep antiquity.
In differential geometry, a cylinder is defined more broadly as any ruled surface spanned by a one-parameter family of parallel lines. A cylinder whosecross section is an ellipse, parabola, or hyperbola is called an elliptic cylinder, parabolic cylinder, or hyperbolic cylinder respectively.
Cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"[1]) is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder. The surface area and the volume of a cylinder have been known since deep antiquity.
In differential geometry, a cylinder is defined more broadly as any ruled surface spanned by a one-parameter family of parallel lines. A cylinder whosecross section is an ellipse, parabola, or hyperbola is called an elliptic cylinder, parabolic cylinder, or hyperbolic cylinder respectively.
5. SPHERE. A sphere (from Greek σφαῖρα -- sphaira, "globe, ball"[1]) is a perfectly round geometrical and circular object in three-dimensional space, such as the shape of a completely round ball. Like a circle, which, in geometrical contexts, is in two dimensions, a sphere is the set of points which are all the same distance r from a given point in space. This distance r is known as the radius of the sphere, and the given point is known as the center of the sphere. The maximum straight distance through the sphere is known as the diameter. It passes through the center and is thus twice the radius.In mathematics, a distinction is made between the sphere (a two-dimensional closed surface embedded in three-dimensional Euclidean space) and the ball (a three-dimensional shape which includes the interior of a sphere).
6. HEXAGONAL PRISM.
In geometry, the hexagonal prism is a prism with hexagonal base. This polyhedron has 8 faces, 18 edges, and 12 vertices.Since it has eight faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces. Because of the ambiguity of the term octahedron and the dissimilarity of the various eight-sided figures, the term is rarely used without clarification.
In geometry, the hexagonal prism is a prism with hexagonal base. This polyhedron has 8 faces, 18 edges, and 12 vertices.Since it has eight faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces. Because of the ambiguity of the term octahedron and the dissimilarity of the various eight-sided figures, the term is rarely used without clarification.
7. SQUARE PYRAMID.
In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it will have C4vsymmetry.
In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it will have C4vsymmetry.
8.RECTANGULAR PRISM.
A solid (3-dimensional) object which has six faces that are rectangles.
It is a prism because it has the same cross-section along a length.
A solid (3-dimensional) object which has six faces that are rectangles.
It is a prism because it has the same cross-section along a length.
9. HEXAGONAL PYRAMID
.In geometry, a hexagonal pyramid is a pyramid with a hexagonal base upon which are erected six triangular faces that meet at a point (the apex). Like any pyramid, it is self-dual.
A right hexagonal pyramid with a regular hexagon base has C6v symmetry.
A right regular pyramid is one which has a regular polygon as its base and whose apex is above the center of the base, so that the apex, the center of the base and any other vertex form a right triangle.
.In geometry, a hexagonal pyramid is a pyramid with a hexagonal base upon which are erected six triangular faces that meet at a point (the apex). Like any pyramid, it is self-dual.
A right hexagonal pyramid with a regular hexagon base has C6v symmetry.
A right regular pyramid is one which has a regular polygon as its base and whose apex is above the center of the base, so that the apex, the center of the base and any other vertex form a right triangle.