Platonic solids

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Name
Tetrahedron
Hexahedron
(Cube)
Octahedron
Dodecahedron
Icosahedron
Picture
Tetrahedron
Hexahedron (Cube)
Octahedron
Dodecahedron
Icosahedron
Net
Tetrahedron net
Hexahedron (Cube) net
Octahedron net
Dodecahedron net
Icosahedron net
Faces
4
6
8
12
20
Face type
equilateral triangle
square
equilateral triangle
equilateral pentagon
equilateral triangle
Duality
tetrahedron
octahedron
hexahedron
icosahedron
dodecahedron
Edges
6
12
12
30
30
Vertices
4
8
6
20
12
Edges from vertex
3
3
4
3
5
Number of diagonals
0
4
3
100
36
Dihedral angle
≈70°31'43,61''
90°
≈109°28'16,39''
≈116°33'55,84''
≈138°11'22,87''
Surface area
3 a 2
6 a 2
2 3 a 2
3 25 + 10 5 a 2
5 3 a 2
Volume
2 a 3 12
a 3
2 a 3 3
( 15 + 7 5 ) a 3 4
( 15 + 5 5 ) a 3 12
Circumradiu
6 a 4
3 a 2
3 a 2
3 ( 1 + 5 ) a 4
10 + 2 5 a 4
Inradiu
6 a 12
a 2
6 a 6
1 2 25 + 11 5 10 a
42 + 18 5 12 a
Midradius
2 a 4
2 a 2
a 2
( 5 + 3 ) a 4
( 1 + 5 ) a 4

Keywords: Platonic solids, also called the regular solids or regular polyhedra
Home Algebra Geometry Mathematical analysis Probability and Statistics
Trigonometry
Law of Sines
Law of Cosines
Trygonometry Identities of same angle
Identities for the sum and difference of two angles
Trigonometric identities of double angles
Trigonometric identities of half angles
Sum and difference of trigonometric functions
Trigonometry Special Angles
Two-dimensional geometric shapes
Basic Proportionality Theorem
Triangle
Special Triangles - Right Triangle, Equilateral Triangles, Isosceles Triangles
Quadrilateral
Squere
Rectangle
Rhombus
Parallelogram
Kite
Trapezoid
Circle
Circular sector
Circular segment
Three-dimensional geometric shapes
Cube
Sphere
Cone
Prism
Pyramide
Platonic solids
Cylinder
Vectors
Scalar Product of Vectors
Vector Product of Vectors
Analytical Geometry 2D
Distance between two points
Circle
Linear equation
Ellipse

Platonic solids