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Radius of inscribed sphere inside regular tetrahedron Calculator

Category Math ↺
Math Geometry ↺
Geometry 3D Geometry ↺
3D-Geometry Platonic Solids ↺
✖The Length of edge of polyhedron. ⓘ Length of edge [a]
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✖A dihedral angle is the angle between two intersecting planes.ⓘ Dihedral Angle [θ]
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-10%
✖The radius of a sphere inscribed around a polyhedron P is called the inradius of Pⓘ Radius of inscribed sphere inside regular tetrahedron [r]
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11 Other formulas that you can solve using the same Inputs

Radius of inscribed sphere inside platonic solids
Radius=Length of edge*0.5*cos(180/Number of edges meeting at a vertex)/(sin(180/Number of edges in a face)*tan(180/Number of edges in a face)*cos(0.5*Dihedral Angle)) GO
Radius of circumscribed sphere around platonic solids
Radius=Length of edge*0.5*sin(180/Number of edges meeting at a vertex)/(sin(180/Number of edges in a face)*cos(0.5*Dihedral Angle)) GO
Radius of inscribed sphere inside the regular dodecahedron
Radius=Length of edge*0.5*cos(180/3)/(sin(180/5)*tan(180/5)*cos(0.5*Dihedral Angle)) GO
Radius of inscribed sphere inside the regular icosahedron
Radius=Length of edge*0.5*cos(180/5)/(sin(180/3)*tan(180/3)*cos(0.5*Dihedral Angle)) GO
Radius of inscribed sphere inside the regular octahedron
Radius=Length of edge*0.5*cos(180/4)/(sin(180/3)*tan(180/3)*cos(0.5*Dihedral Angle)) GO
Radius of inscribed sphere inside the cube
Radius=Length of edge*0.5*cos(180/3)/(sin(180/4)*tan(180/4)*cos(0.5*Dihedral Angle)) GO
Radius of circumscribed sphere in a regular dodecahedron
Radius=Length of edge*0.5*sin(180/3)/(sin(180/5)*cos(0.5*Dihedral Angle)) GO
Radius of circumscribed sphere in a regular icosahedron
Radius=Length of edge*0.5*sin(180/5)/(sin(180/3)*cos(0.5*Dihedral Angle)) GO
Radius of circumscribed sphere in a regular octahedron
Radius=Length of edge*0.5*sin(180/4)/(sin(180/3)*cos(0.5*Dihedral Angle)) GO
Radius of circumscribed sphere in regular tetrahedron
Radius=Length of edge*0.5*sin(180/3)/(sin(180/3)*cos(0.5*Dihedral Angle)) GO
Radius of circumscribed sphere in a cube
Radius=Length of edge*0.5*sin(180/3)/(sin(180/4)*cos(0.5*Dihedral Angle)) GO

5 Other formulas that calculate the same Output

Radius of inscribed sphere inside platonic solids
Radius=Length of edge*0.5*cos(180/Number of edges meeting at a vertex)/(sin(180/Number of edges in a face)*tan(180/Number of edges in a face)*cos(0.5*Dihedral Angle)) GO
Radius of inscribed sphere inside the regular dodecahedron
Radius=Length of edge*0.5*cos(180/3)/(sin(180/5)*tan(180/5)*cos(0.5*Dihedral Angle)) GO
Radius of inscribed sphere inside the regular icosahedron
Radius=Length of edge*0.5*cos(180/5)/(sin(180/3)*tan(180/3)*cos(0.5*Dihedral Angle)) GO
Radius of inscribed sphere inside the regular octahedron
Radius=Length of edge*0.5*cos(180/4)/(sin(180/3)*tan(180/3)*cos(0.5*Dihedral Angle)) GO
Radius of inscribed sphere inside the cube
Radius=Length of edge*0.5*cos(180/3)/(sin(180/4)*tan(180/4)*cos(0.5*Dihedral Angle)) GO

Radius of inscribed sphere inside regular tetrahedron Formula

Radius=Length of edge*0.5*cos(180/3)/(sin(180/3)*tan(180/3)*cos(0.5*Dihedral Angle))
More formulas
Volume of a Cube GO
Surface Area of a Cube GO
Volume of Regular Dodecahedron GO
Volume of Regular Icosahedron GO
Volume of Regular Octahedron GO
Volume of Regular Tetrahedron GO
Surface Area of Dodecahedron GO
Surface Area of Icosahedron GO
Surface Area of Regular Octahedron GO
Surface Area of Regular Tetrahedron GO
Dihedral Angle of Platonic Solids GO
Radius of circumscribed sphere in regular tetrahedron GO
Radius of circumscribed sphere around platonic solids GO
Radius of circumscribed sphere in a cube GO
Radius of circumscribed sphere in a regular octahedron GO
Radius of circumscribed sphere in a regular dodecahedron GO
Radius of circumscribed sphere in a regular icosahedron GO
Radius of inscribed sphere inside platonic solids GO
Radius of inscribed sphere inside the regular octahedron GO
Radius of inscribed sphere inside the regular dodecahedron GO
Radius of inscribed sphere inside the regular icosahedron GO
Surface Area of Platonic Solids GO
Volume of Platonic Solids GO
Edge of Regular Octahedron GO

What is Tetrahedron?

in geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedral and the only one that has fewer than 5 faces.

How to Calculate Radius of inscribed sphere inside regular tetrahedron?

Radius of inscribed sphere inside regular tetrahedron calculator uses Radius=Length of edge*0.5*cos(180/3)/(sin(180/3)*tan(180/3)*cos(0.5*Dihedral Angle)) to calculate the Radius, Radius of inscribed sphere inside regular tetrahedron is called the inradius of the regular tetrahedron. Radius and is denoted by r symbol.

How to calculate Radius of inscribed sphere inside regular tetrahedron using this online calculator? To use this online calculator for Radius of inscribed sphere inside regular tetrahedron, enter Dihedral Angle (θ) and Length of edge (a) and hit the calculate button. Here is how the Radius of inscribed sphere inside regular tetrahedron calculation can be explained with given input values -> 0.166673 = 1*0.5*cos(180/3)/(sin(180/3)*tan(180/3)*cos(0.5*1)).

FAQ

What is Radius of inscribed sphere inside regular tetrahedron?
Radius of inscribed sphere inside regular tetrahedron is called the inradius of the regular tetrahedron and is represented as r=a*0.5*cos(180/3)/(sin(180/3)*tan(180/3)*cos(0.5*θ)) or Radius=Length of edge*0.5*cos(180/3)/(sin(180/3)*tan(180/3)*cos(0.5*Dihedral Angle)). A dihedral angle is the angle between two intersecting planes and The Length of edge of polyhedron. .
How to calculate Radius of inscribed sphere inside regular tetrahedron?
Radius of inscribed sphere inside regular tetrahedron is called the inradius of the regular tetrahedron is calculated using Radius=Length of edge*0.5*cos(180/3)/(sin(180/3)*tan(180/3)*cos(0.5*Dihedral Angle)). To calculate Radius of inscribed sphere inside regular tetrahedron, you need Dihedral Angle (θ) and Length of edge (a). With our tool, you need to enter the respective value for Dihedral Angle and Length of edge and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Radius?
In this formula, Radius uses Dihedral Angle and Length of edge. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Radius=Length of edge*0.5*cos(180/Number of edges meeting at a vertex)/(sin(180/Number of edges in a face)*tan(180/Number of edges in a face)*cos(0.5*Dihedral Angle))
  • Radius=Length of edge*0.5*cos(180/4)/(sin(180/3)*tan(180/3)*cos(0.5*Dihedral Angle))
  • Radius=Length of edge*0.5*cos(180/3)/(sin(180/4)*tan(180/4)*cos(0.5*Dihedral Angle))
  • Radius=Length of edge*0.5*cos(180/3)/(sin(180/5)*tan(180/5)*cos(0.5*Dihedral Angle))
  • Radius=Length of edge*0.5*cos(180/5)/(sin(180/3)*tan(180/3)*cos(0.5*Dihedral Angle))
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