Geometric Shapes Guide

Every 2D shape's sides, vertices, diagonals and angles; every 3D solid's faces, edges and vertices — with real-life examples and sourced numbers.

The difference between 2D and 3D shapes

A 2D (two-dimensional) shape is flat — it has length and width but no thickness, like a circle or square drawn on paper. A 3D (three-dimensional) shape, or solid, also has depth — like a sphere or cube you could actually hold. This distinction is US Common Core standard K.G.3, and part of Turkey's Grade 1 curriculum (MAT.1.3.5).

Try It Yourself: Rotate a Solid

Pick a solid, change its style, rotate and zoom it in real 3D — falls back automatically to a fixed-angle drawing if WebGL isn't available, nothing breaks.

Solid

Style

🧊 Real 3D (WebGL)loading…

Color

Size100%

Rotation-28°

Camera Angle26°

2D Shapes: Sides, Vertices, Diagonals and Angles

Diagonals = n(n − 3) ÷ 2 and the interior angle sum = (n − 2) × 180°, where n is the number of sides — for a regular polygon, each angle is the sum divided by the number of sides.

Shape	Sides	Vertices	Diagonals	Angle Sum	Each Angle (Regular)	Symmetry Lines
CircleNot a polygon — no straight sides or vertices. "Çember" is the outline, "daire" the filled region.	—	—	—	—	—	—
Oval / Ellipse	—	—	—	—	—	2
Triangle3 lines of symmetry only if equilateral.	3	3	0	180°	60°	3
Square	4	4	2	360°	90°	4
Rectangle	4	4	2	360°	90°	2
Rhombus	4	4	2	360°	—	2
ParallelogramNo line of symmetry — only 180° rotational symmetry.	4	4	2	360°	—	0
Trapezoid (US) / Trapezium (UK)1 line of symmetry if isosceles. US "trapezoid" = UK "trapezium" — the names are swapped between the two.	4	4	2	360°	—	0
Kite	4	4	2	360°	—	1
Pentagon	5	5	5	540°	108°	5
Hexagon	6	6	9	720°	120°	6
Heptagon	7	7	14	900°	128.57°	7
Octagon	8	8	20	1080°	135°	8
Nonagon	9	9	27	1260°	140°	9
Decagon	10	10	35	1440°	144°	10
Star (5-point)A 10-sided concave shape, not a simple convex polygon — the diagonal/angle-sum formulas for convex polygons don't apply directly.	10	10	—	—	—	5

The Quadrilateral Family

Square, rectangle, rhombus, parallelogram, trapezoid and kite all share 4 sides, 4 vertices and 2 diagonals, but differ in their angle and symmetry rules. Every square is a rectangle (it meets the 4-right-angles rule), but not every rectangle is a square. Whether a parallelogram counts as a trapezoid depends on the definition used: yes under "at least one pair of parallel sides", no under the "exactly one pair" definition more common in Turkish ("yamuk") textbooks.

3D Solids: Faces, Edges and Vertices

"Flat faces" and "curved surfaces" are separate columns, so this avoids the "2 or 3" argument for a cylinder: it has 2 flat faces AND 1 curved surface — whether you add them together is a convention choice.

Solid	Flat Faces	Curved Surfaces	Edges	Vertices	Real-Life Example
Cube	6	—	12	8	dice, sugar cube, Rubik's cube
Rectangular Prism (Cuboid)	6	—	12	8	book, brick, cereal box
Triangular Prism	5	—	9	6	camping tent, a Toblerone bar
Hexagonal Prism	8	—	18	12	an unsharpened pencil, a nut (hardware)
Square Pyramid	5	—	8	5	the Egyptian pyramids, a tent with a square base
Cylinder	2	1	2	0	a can, a battery, a candle
Cone	1	1	1	1	an ice cream cone, a traffic cone
Sphere	0	1	0	0	a ball, a globe, a marble
Hemisphere	1	1	1	0	a dome, a bowl turned upside down

The sphere isn't shown as a separate row here because it has 0 flat faces, 1 curved surface, 0 edges and 0 vertices — with no flat face at all, it's honestly excluded from "which 2D shape is this solid's face" questions (as in the Math Worksheet tool's "Faces of Solids" topic).

Bonus: The Platonic Solids

The 5 special polyhedra where every face is the same regular polygon. All five check out against Euler's formula (Faces + Vertices − Edges = 2).

Solid	Face Shape	Faces	Edges	Vertices	Euler (F+V−E)
Tetrahedron (triangular pyramid)	triangle	4	6	4	2
Cube (hexahedron)	square	6	12	8	2
Octahedron	triangle	8	12	6	2
Dodecahedron	pentagon	12	30	20	2
Icosahedron	triangle	20	30	12	2

Turn These Shapes Into Printables

Every solid drawn above comes from the same vector module used in two tools: Math Worksheet's "3D Shape Recognition/Matching", "Faces of Solids" and "Real-World Objects & Shapes" topics (Kindergarten, K.G.1/K.G.2/K.G.4), and Photo to Coloring Page's ready-template gallery under "3D Solids" and "2D Shapes".

Frequently Asked Questions

How many faces, edges and vertices does a cube have?

6 faces, 12 edges, 8 vertices. Check it with Euler's formula: faces + vertices − edges = 6 + 8 − 12 = 2, which holds for every convex polyhedron.

How many faces does a cylinder have — 2 or 3?

Both answers are used. Most K-5 material says 2 (the top and bottom flat circles) plus 1 curved surface. Some sources count the curved surface as a third "face", making it 3 faces and 0 edges instead of 2 edges. Neither is wrong — they're just counting curved surfaces differently, so this page lists flat faces and curved surfaces separately.

Does a cone have an edge, and how many vertices?

A cone has 1 vertex (the apex) and 1 flat circular face. Whether the curved boundary where the circle meets the surface counts as an "edge" is a convention choice — most K-5 charts count it as 1 curved edge; some (like Cuemath) count 0 straight edges.

What is the difference between 2D and 3D shapes?

A 2D (two-dimensional) shape is flat — it has length and width but no thickness, like a circle or a square drawn on paper. A 3D (three-dimensional) shape, or solid, also has depth — like a sphere or a cube you could actually hold. This is CCSS Kindergarten standard K.G.3.

What are polygons called by number of sides?

3 = triangle, 4 = quadrilateral, 5 = pentagon, 6 = hexagon, 7 = heptagon, 8 = octagon, 9 = nonagon, 10 = decagon, 12 = dodecagon. Beyond 12 sides, shapes are usually just called "n-gons" (for example a 15-gon).

How do you find the number of diagonals in a polygon?

Diagonals = n(n − 3) ÷ 2, where n is the number of sides. A hexagon (n = 6) has 6 × 3 ÷ 2 = 9 diagonals.

What is Euler's formula for 3D shapes?

For any convex polyhedron: Faces + Vertices − Edges = 2. A square pyramid checks out as 5 + 5 − 8 = 2, and a triangular prism as 5 + 6 − 9 = 2.

Is a square a rectangle, and is a parallelogram a trapezoid?

Yes to the first — every square meets a rectangle's definition (4 right angles), so a square is a special rectangle. The second depends on which definition of trapezoid is used: under the "at least one pair of parallel sides" (inclusive) definition a parallelogram is a trapezoid, but under the "exactly one pair" (exclusive) definition — more common in Turkish ("yamuk") textbooks — it isn't.

Sources

Every number on this page is either computed from a formula (2D diagonals/angles) or cross-checked against the sources below. Where sources genuinely disagree on a convention (like a cylinder's face count), that's stated openly in the FAQ rather than picking one number and hiding the disagreement.