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The Insphere Radius of a Deltoidal Icositetrahedron is the radius of the sphere that is contained by the Deltoidal Icositetrahedron in such a way that all the faces just touch the sphere. This sphere is tangent to all the faces of the polyhedron.
The calculator uses the formula:
Where:
Explanation: The formula calculates the radius of the largest sphere that can fit inside the Deltoidal Icositetrahedron, touching all its faces.
Details: Calculating the insphere radius is important in geometry and 3D modeling as it helps understand the spatial properties of the polyhedron and its relationship with inscribed spheres.
Tips: Enter the Long Edge of Deltoidal Icositetrahedron in meters. The value must be positive and greater than zero.
Q1: What is a Deltoidal Icositetrahedron?
A: A Deltoidal Icositetrahedron is a Catalan solid with 24 deltoid faces, 26 vertices, and 48 edges.
Q2: How is the insphere radius different from the circumsphere radius?
A: The insphere radius is the radius of the sphere inside the polyhedron that touches all faces, while the circumsphere radius is the radius of the sphere that contains the polyhedron with all vertices on the sphere.
Q3: What are the applications of this calculation?
A: This calculation is used in geometry, crystallography, architecture, and 3D modeling where precise spatial relationships are important.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Deltoidal Icositetrahedron. Other polyhedra have different formulas for calculating their insphere radii.
Q5: What units should I use for the calculation?
A: The calculator uses meters, but you can use any consistent unit of length as the formula is dimensionally consistent.