Names of Geometric Shapes—With Pictures
Most children know the names of basic two-dimensional shapes before they enter school. Squares, triangles, circles, and ovals are easy for young children to recognize and draw, even if their other math skills are still developing.
As they get older, they can discern more differences among shapes and start to learn more precise words for the wide variety of geometric objects they encounter in life. Soon, they begin to learn names of three-dimensional figures like cubes, cones, cylinders, spheres, and more. The following list of shapes covers both common and more rare geometrical figures. To make learning their names easier, each shape name is accompanied by a picture.
Flat (Two-Dimensional) Figures With Curves
- Circle A circle is a closed curve with constant curvature. The distance from the center to the border is constant, no matter where the point is on the border. Technically speaking, a "circle" refers to the curved boundary, while a "disk" is a circle plus its interior. In everyday life, the two terms can be used interchangeably.
- Ellipse An ellipse is a circle squished (or stretched) in one direction. If you cut a cone or a cylinder at an angle, the cross-section is an ellipse. An ellipse has two foci with the following property: For any triangle you draw that connects the two foci and an arbitrary point on the ellipse's border, the perimeter of the triangle is constant. A circle is a special type of ellipse in which the two foci coincide at the same point.
- Stadium A stadium is an oblong figure formed by joining semicircles to opposite ends of a rectangle. It gets its name from the shape of sports fields.
- Oval An oval is a non-specific term for any closed oblong or egg-shaped curve without pointed corners along its perimeter. It includes ellipses, stadiums, and more irregular egg-shaped curves.
- Arch An arch is a shape with one curved side opposite a straight edge. It may have more than one straight side. A common arch shape is a half-circle attached to a rectangle. "Arch" and "arc" are somewhat interchangeable. Arch is a term used in engineering and architecture; arc is a mathematical term that means a finite length of curve, not a closed figure.
- Circular Sector A circular sector is a wedge or pie slice cut from a circle. The vertex of a circular sector is the center of the circle from which it is cut.
- Circular Segment A circular segment is formed by cutting a circle along a chord. It is a two-sided shape, with one side curved and the other side straight. Arches can be shaped like circular segments
- Lens A lens is a two-sided figure formed from two arcs; both arcs are convex with respect to the interior of the figure. It has two vertices where the arcs meet.
- Crescent A crescent is a two-sided figure formed from two arcs; one curved side is convex with respect to the interior, and the other is concave. It can be formed by taking a disk and removing a smaller disk along the edge. A lune is a particular type of crescent whose arcs are circular arcs.
- Annulus An annulus is a ring. It is formed by taking a disk and removing a smaller disk from the center.
Other Curved Shapes
- Egg An egg shape is an oval that has one end with a much smaller radius of curvature than the rest of the shape.
- Trefoil A trefoil has three curved lobes spaced equally. It looks like an equilateral triangle with arcs attached to the sides. Some trefoil curves have pointed leaves.
- Quatrefoil A quatrefoil has four equally spaced curved lobes. It looks like a square with arcs attached to the sides. Some quatrefoil curves have pointed leaves.
- Cinquefoil A cinquefoil has five equally spaced curve lobes. It looks like a regular pentagon with arcs attached to the sides.
- Nephroid A nephroid looks like a circle or oval that has been indented into two points on opposite sides. Alternatively, it looks like two overlapping ovals.
- Teardrop A teardrop shape looks like an oval with one end pointed outward. It may be completely convex, or it may become concave as it nears the point. A completely convex teardrop shape may be called a folium.
- Kidney A kidney shape or bean shape is a closed curve with no points that looks like an oval indented on one side.
- Heart A heart is a closed curve with one concave point and one convex point on opposite sides.
- Cardioid A cardioid looks like a circle but with a point indented inward.
- Triangle A triangle is a three-sided figure. One property of triangles is that all three angles add up to 180 degrees. The longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.
- Scalene Triangle A scalene triangle has three sides of unequal length. All three angles are also unequal.
- Isosceles Triangle A triangle with two sides of equal length and a third side that is either longer or shorter than the other two. Because two sides are equal, the angles opposite these sides are also equal.
- Equilateral Triangle A triangle with three equal sides and three equal angles. Also called an equiangular triangle, each of the angles is 60 degrees.
- Obtuse Triangle A triangle that has one angle with a measure greater than 90 degrees, A.K.A. an obtuse angle. The other two angles are necessarily less than 90 degrees.
- Right Triangle A triangle with one angle that is exactly 90 degrees, A.K.A. a right angle. The other two angles add up to 90 degrees.
- Acute Triangle A triangle whose three angles are all less than 90 degrees, A.K.A. acute angles.
- Quadrilateral Any four-sided figure with straight edges.
- Parallelogram A four-sided figure that has two pairs of parallel sides. Opposite sides are equal in length, and opposite angles are equal as well.
- Rectangle A parallelogram with four right angles.
- Rhombus A parallelogram with four equal sides. See also, Rhombus Area Formula.
- Trapezoid A quadrilateral with one pair of parallel sides.
- Kite A quadrilateral with two pairs of sides that have equal length. The sides with equal length are adjacent to one another, rather than opposite as with a parallelogram.
- Square A rectangle that is also a rhombus. It has four equal sides and four equal angles that measure 90 degrees each.
- Pentagon A pentagon is a five-sided polygon. A regular pentagon has five equal sides and five equal angles.
- Hexagon A hexagon is a six-sided polygon. See also, Regular Hexagon Area Formula.
- Heptagon A heptagon is a seven-sided polygon.
- Octagon An octagon is an eight-sided polygon. A stop sign is in the shape of a regular octagon since it has eight equal sides and eight equal angles.
- Nonagon A nonagon is a nine-sided polygon.
- Decagon A decagon is a ten-sided polygon.
- Hendecagon Occasionally called an undecagon, this is a polygon with 11 sides.
- Regular Polygon A regular polygon is a polygon with equal side lengths and equal angles at the vertices.
- Convex Polygon For convex polygons, all vertex angles as measured from the interior are less than 180 degrees. Equivalently, all vertex angles measured from the exterior are greater than 180 degrees.
Solid Shapes With Curved Surfaces
- Sphere A sphere is the three-dimensional analogue of a disk. The boundary of a sphere is a three-dimensional closed curved surface such that every point on the surface is equidistant from the center.
- Ellipsoid The three-dimensional analogue of an ellipse, it can be thought of as a sphere that has been squished or stretched in one or two directions. If two of the three axes have equal length it is called a spheroid. See Ellipsoid Surface Area Formula.
- Cone A cone has a circular base that tapers linearly to a point, called the apex. If the tip is sliced off, the resulting shape is called a conical frustum.
- Cylinder A cylinder has two circular bases of equal size at the ends, and a middle section that can be formed by rolling a rectangle into a tube. It is the standard shape for canned foods. A conical frustum is like a cylinder except that the circular ends are different sizes.
- Barrel Like a cylinder, both ends of a barrel are circles of equal size. But unlike a cylinder, its sides do not go straight up and down, but rather bulge outward in the middle.
- Torus A torus is the technical mathematical term for a doughnut or bagel shape.
- Dome - A dome is any solid shape that has a flat base and a curved surface connecting the boundary of the base. A hemisphere (sphere cut in two) is a type of dome, as is a spherical cap.
- Triangular Prism A triangular prism is a solid shape with two equal triangular faces on opposite ends oriented in the same direction and parallel. Three parallelograms connect the matching triangular edges. If the parallelograms are rectangles, it is called a right prism. Otherwise it is called an oblique prism.
- Rectangular Prism A rectangular prism is a solid shape with six rectangular faces. Opposite faces have the same shape, size, and orientation and are parallel.
- Cube A regular rectangular prism; all faces are squares of equal size. It has six faces, eight vertices, 12 edges, and is one of the five Platonic solids.
- Parallelepiped A generalization of a rectangular prism in which all the faces are parallelograms, but not necessarily rectangles. A parallelepiped has six faces that come in parallel pairs.
- Pentagonal Prism A pentagonal prism has two equal pentagonal faces on opposite ends oriented in the same direction and parallel to one another. Five parallelogram faces connect the matching pentagonal edges. In the case of a right prism, the parallelograms are rectangles.
- Hexagonal Prism A solid shape with two equal hexagonal faces on opposite ends oriented in the same direction and parallel. Six parallelogram faces connect the matching hexagonal edges.
- Tetrahedron Also called a triangular pyramid, this shape has four triangular faces, four vertices, and six edges. If the triangles are equilateral, it is a Platonic solid.
- Square Pyramid A pyramid with a square base and four triangular faces that meet at a point opposite to the square base.
- Pentagonal Pyramid A pyramid with a pentagonal base and five triangular faces that meet at a point opposite to the base.
- Hexagonal Pyramid A pyramid with a hexagonal base and six triangular faces that meet at a point opposite to the base.
- Octahedron A solid shape with eight triangular faces, six vertices, and 12 edges. Each vertex is the meeting point of four triangles. If the triangles are equilateral, it is one of the Platonic solids.
- Dodecahedron Any solid shape with 12 faces. A pentagonal dodecahedron is a Platonic solid with 12 regular pentagonal faces, 20 vertices, and 30 edges, where each vertex is the meeting point of three pentagons. But not all dodecahedrons have pentagonal faces. For example, a rhombic dodecahedron's 12 faces are rhombuses.
- Icosahedron A solid shape with 20 triangular faces, 12 vertices, and 30 edges. Each vertex is the meeting point of five triangles. If the triangles are equilateral, it is one of the Platonic solids.
- Platonic Solid A polyhedron whose faces are regular polygons of the same shape and size and whose vertices all have the same degree, i.e., at every corner there are the same number of polygon faces meet. There are only five Platonic solids: tetrahedron, cube, octohedron, dodecahedron, icosahedron. The cube and octahedron are duals, as are the icosahedron and dodecahedron. The tetrahedron is dual with itself.
- Archimedean Solid An Archimedean solid is composed of two or more regular polygons, and all of its vertices are identical, i.e., each corner is composed of the same number of and type of polygonal vertices. Examples include the cuboctahedron, rhombicuboctahedron, and icosidodecahedron. The dual of an Archimdean solid is a Catalan solid.
- Catalan Solid Defined as duals of Archimedean solids, Catalan solids consist of one type of irregular polygon, but the vertices are not all identical. The dual of a Catalan solid is an Archimedean solid, and a Catalan solid has as many different types of vertices as its dual has different types of faces. Examples include the rhombic dodecahedron, deltoidal icositetrahedron, and rhombic triacontahedron.
- Polyhedral Dual If P and Q are two polyhedra that are dual with one another, then the faces of P correspond to the vertices of Q, and the vertices of P correspond to the faces of Q. The edges of dual polyhedra are in one-to-one correspondence. Some dual pairs include the cuboctahedron and rhombic dodecahedron, the rhombicuboctahedron and deltoidal icositetrahedron, and the icosidodecahedron and rhombic triacontahedron.
All the drawings of two-dimensional shapes and polyhedra in this article (except the octahedron, icosahedron, dodecahedron, and rhombic dodecahedron) were created by the author. Transparent images of the octahedron, icosahedron, dodecahedron, and rhombic dodecahedron are courtesy of Wikimedia Commons. Pictures of other three-dimensional shapes are courtesy of free stock photo resources. You can create polygons in free programs such as MS Paint, Geogebra, GIMP, or Pixlr.com, a free online image editing program.
Best Geometry Toy for Toddlers: Melissa and Doug Wooden Shape Sorting Cube
This is a well-made wooden sorting box with sliding top and 12 wooden shape blocks painted in durable, bright colors. The shapes included are a square, rectangle, triangle, pentagon, hexagon, octagon, parallelogram, trapezoid, quatrefoil, five-pointed star, oval, and rhombus.