1. Reuleaux triangle
   Hyperboloid
2. Rectangle
   Balbis

Rectangles are parallelograms with four straight sides and four interior right angles at 90 degrees. In this quadrilateral, the opposite sides are parallel to each other and are of the same length.

1. Pentagon
   Torus
2. Möbius strip
   Lemniscate

A pentagon is a type of polygon with five sides and five internal angles, which amount to a total of 520 degrees in a simple pentagon. Extending the sides of a pentagon until they intersect creates a pentagram or five-pointed star.

1. Hemihilex
   Square
2. Apollonian gasket
   Catenary curve

A square is a flat shape with four sides, all of which have the same length and contain right angles of 90 degrees. Squares are examples of regular polygons and quadrilaterals. Some cement blocks, chess boards and even waffles are square.

1. Cylinder
   Balbis
2. Vesica piscis
   Pentominoes

A cylinder is a three-dimensional object with two circular flat ends. It has a circular or oval cross-section and parallel sides. Objects such as batteries, water tanks and pipes are cylindrical.

1. Truncated icosahedron
   Trapezoid
2. Pentagram
   Oblate spheroid

A trapezoid has four sides; it is a flat shape and has two opposite sides that are parallel to each other. These parallel sides are called "bases." The other sides are referred to as legs, and these are not parallel to one another.

1. Squircle
   Hyperboloid
2. Heart
   Heptagram

The heart is an ideographic symbol used to express feelings and emotions, such as love - particularly romantic love. The heart symbol is usually depicted in red, which is traditionally used to represent passion and strong emotions.

1. Balbis
   Reuleaux triangle
2. Möbius strip
   Oval

The oval is a geometric shape that is similar to a circle, except that one part of the shape is wider than the other side. This two-dimensional plane resembles an ellipse or the outline of an egg.

1. Triangular pyramid
   Vesica piscis
2. Lemniscate
   Apollonian gasket

This type of pyramid has one triangle as the base which supports three triangular faces that meet at a common point known as an apex. This three-dimensional shape can be regular, with sides of equal length, or irregular, with sides of different lengths.

1. Truncated icosahedron
   Hemihilex
2. Cube
   Oblate spheroid

A cube is a regular solid that has six equal sides or faces, three of which connect at each vertex. It is a three-dimensional depiction of the square, with eight vertices and 12 edges. Dice and a child's block set are examples of cubes.

1. Pentominoes
   Hyperboloid
2. Circle
   Pentagram

A circle is a simple plane figure which is two-dimensional and round. To create a circle, a curve must be drawn and every point must be the same distance from the center. Circles are all around us, such as the face of a watch or the shape of a pizza.

1. Triquetra
   Triangular prism
2. Catenary curve
   Squircle

This three-dimensional triangular prism is a polyhedron - meaning that it has many plane faces - five to be precise. Three of these faces are rectangular, while the other two are triangles. Triangular roofs, camping tents and Toblerone chocolate are all examples of triangular prisms.

1. Vesica piscis
   Balbis
2. Hemihilex
   Isosceles triangle

This type of triangle consists of two equal sides, with the angles opposite those equal sides being equal. The equal sides in an isosceles triangle are called legs, while the third side is referred to as the base. Isosceles triangles can be found in architecture, such as on the steeple of a church.

1. Balbis
   Reuleaux triangle
2. Torus
   Deltoid

The deltoid shown here is a kite - a quadrilateral with two pairs of neighboring equal sides. Another kind of deltoid, known as a Steiner curve or tricuspid, is roughly triangular in shape and is joined by three inward curves. The most common example of the deltoid is the deltoid muscle.

1. Equilateral triangle
   Hyperboloid
2. Möbius strip
   Lemniscate

An equilateral triangle is one where all internal angles and sides are of equal size and length. The interior angles are 60 degrees each and sum up to 180 degrees. An equilateral triangle is an example of a regular polygon.

1. Heptagram
   Hexagon
2. Truncated icosahedron
   Oblate spheroid

A regular hexagon is a polygon with six equal sides and six equal angles which are 120 degrees, amounting to a sum of 720 degrees. Due to its properties, six equilateral triangles can be made from a regular hexagon. Nuts and bolt heads are hexagonal.

1. Balbis
   Pentominoes
2. Apollonian gasket
   Rhombus

Any quadrilateral with four equal sides and the opposite sides parallel is called a rhombus. In this parallelogram, angles which are opposite to each other are equal.

1. Pentagram
   Vesica piscis
2. Octahedron
   Catenary curve

An octahedron is a Platonic solid with eight faces/sides, six points and twelve edges. In a regular octahedron, the eight sides form equilateral triangles, with four of them meeting at every corner. An eight-sided die is an example of an octahedron.

1. Square
   Tetrahedron
2. Circle
   Cube

A tetrahedron, or triangular pyramid as it is usually called, is a polyhedron that has four triangle-shaped faces, six straight edges and four vertices. This 3-D shape is the only polyhedral with fewer than five faces.

1. Sphere
   Torus
2. Hemihilex
   Balbis

A sphere is a round solid that has perfect symmetry, meaning that it can create two perfect halves when divided. Spheres have no vertices or edges and only have one surface.

1. Oblate spheroid
   Möbius strip
2. Hyperboloid
   Right triangle

A right triangle is a triangle with three sides and a 90-degree angle where two of these sides connect. This triangle is one of the most common geometric shapes and is also the basis of the Pythagorean Theorem.

1. Squircle
   Pentominoes
2. Reuleaux triangle
   Cuboid

Cuboids, with six quadrilateral sides or faces, are more or less boxes. All rectangular cuboids are rectangular prisms.

1. Balbis
   Vesica piscis
2. Cone
   Lemniscate

A cone is a geometric pyramid shape with a circular base. Cones, which may be hollow or solid in geometry, are seen in real life as ice cream cones or as traffic cones placed along roads.

1. Ellipse
   Catenary curve
2. Torus
   Apollonian gasket

An ellipse is a curve that has a regular oval shape. This squished looking circle has focal points F and G which are equal in distance. This means that when moving from point F to any point in the ellipse and then traveling to point G, the distance is always the same.

1. Scalene triangle
   Möbius strip
2. Pentagram
   Truncated icosahedron

A scalene triangle is a type of triangle with three sides - all of which are unequal in length. The angles are also of different sizes and degrees. The shortest side in a scalene triangle is opposite the smallest angle. Similarly, the largest angle is opposite the longest side.

1. Nonagon
   Hyperboloid
2. Balbis
   Hemihilex

A regular nonagon is a shape with nine equal sides and angles that are also equal, with each measuring 140 degrees. The nonagon is a 2-D shape with nine edges and vertices.

1. Vesica piscis
   Reuleaux triangle
2. Star
   Oblate spheroid

The star, or star pentagon or pentagram, has ten edges and two sets of five vertices. The star symbol is used frequently to signify success in life and to represent the star in astronomy.

1. Balbis
   Pentominoes
2. Torus
   Kite

The kite is a quadrilateral that has two pairs of equal straight lines that are adjacent to each other. Kites are also called deltoids. The name "kite" is a type of bird but is more commonly known as the toy that is usually flown in the air.

1. Star
   Kite
2. Heart
   Dodecagon

A dodecagon, also known as a 12-gon, is a figure with twelve sides. A regular dodecagon has twelve equal sides. All angles in a regular dodecagon measure 150 degrees and amount to a sum of 1,800 degrees. Some coins are 12-sided.

1. Annulus
   Möbius strip
2. Lemniscate
   Truncated icosahedron

The word "annulus" stays true to its Latin origin, where it means "little ring." This ring-shaped object is a type of circle with a hole in the middle, much like a regular donut. The edges of an annulus are two circles with one common center.

1. Hyperboloid
   Heptagon
2. Apollonian gasket
   Catenary curve

A heptagon is a type of polygon that has seven sides and angles. A regular heptagon has sides and angles all of the same length and size. The sum of all interior angles in a heptagon is 900 degrees, which means that all interior angles must measure approximately 128.57 degrees.

1. Squircle
   Obtuse triangle
2. Oblate spheroid
   Heptagram

An obtuse triangle is one which has an angle of more than 90 degrees - that angle is obtuse. This triangle also has two other angles measuring less than 90 degrees - they are acute angles. The sum of all angles in a triangle is 180 degrees.

1. Hemihilex
   Vesica piscis
2. Pentagram
   Trapezium

A trapezium is a quadrilateral which has no parallel sides. Also, all four sides of this flat shape are of varying lengths. If a quadrilateral has one pair of parallel sides, it is called a trapezoid instead.

1. Parallelogram
   Reuleaux triangle
2. Balbis
   Pentominoes

A parallelogram is a type of quadrilateral that has two pairs of parallel sides. These opposite sides and angles are congruent - they are of the same length and size. The consecutive or neighboring angles are supplementary, meaning they add up to 180 degrees.

1. Lemniscate
   Octagon
2. Torus
   Möbius strip

An octagon is an eight-sided figure, with eight angles and vertices. The interior angles in a regular octagon are 135 degrees each and amount to 1,080 degrees in total. Stop signs and some umbrellas are in the shape of an octagon.

1. Balbis
   Hyperboloid
2. Lens
   Apollonian gasket

A lens is a shape that is made up of two circular arcs. The important thing about this shape is that in order for it to truly be considered a lens, both arcs must bow outwardly.

1. Truncated icosahedron
   Oblate spheroid
2. Catenary curve
   Ellipsoid

An ellipsoid is like a deformed sphere that can be made by what is called an affine transformation. An ellipsoid is a solid, 3-D depiction of an ellipse and has the cross-sections of an ellipse. The planet Earth has a slight similarity to the ellipsoid shape

1. Pentagram
   Hemihilex
2. Decagon
   Vesica piscis

A regular decagon or 10-gon is a figure with ten angles and sides of equal size and length. All interior angles in a regular decagon measure 144 degrees and sum up to 1,440 degrees. Some above-ground swimming pools are shaped like a decagon.

1. Möbius strip
   Balbis
2. Crescent
   Reuleaux triangle

A crescent is a shape that is thin and curved, with a thick midsection that diminishes and becomes thin at each end. The crescent is one of the shapes the moon assumes during the lunar phase.

1. Apollonian gasket
   Hyperboloid
2. Square pyramid
   Torus

A square pyramid is a 3-D geometric shape that has a square as the base of the pyramid. In this way, it differs from other types of pyramids that have a triangular base. The square pyramid is also a pentahedron because it has five plane faces.