Nonsymmetry Diagonal Of Deltoidal Icositetrahedron Given Insphere Radius Calculator

Formula Used:

\[ d_{Non\ Symmetry} = \frac{\sqrt{4 + 2\sqrt{2}}}{2} \times \frac{r_i}{\sqrt{\frac{22 + 15\sqrt{2}}{34}}} \]

NonSymmetry Diagonal (d_{Non Symmetry}):

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1. What is NonSymmetry Diagonal of Deltoidal Icositetrahedron?

NonSymmetry Diagonal of Deltoidal Icositetrahedron is the length of the diagonal which divides the deltoid faces of Deltoidal Icositetrahedron into two isosceles triangles. It's an important geometric property of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{Non\ Symmetry} = \frac{\sqrt{4 + 2\sqrt{2}}}{2} \times \frac{r_i}{\sqrt{\frac{22 + 15\sqrt{2}}{34}}} \]

Where:

\( d_{Non\ Symmetry} \) — NonSymmetry Diagonal (m)
\( r_i \) — Insphere Radius (m)
\( \sqrt{} \) — Square root function

Explanation: This formula relates the non-symmetry diagonal length to the insphere radius through mathematical constants derived from the geometry of the deltoidal icositetrahedron.

3. Importance of NonSymmetry Diagonal Calculation

Details: Calculating the non-symmetry diagonal is important for understanding the geometric properties of deltoidal icositetrahedrons, which are used in various mathematical and engineering applications, particularly in crystallography and structural design.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding non-symmetry diagonal length.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Icositetrahedron?
A: A deltoidal icositetrahedron is a Catalan solid with 24 deltoid (kite-shaped) faces. It's the dual polyhedron of the rhombicuboctahedron.

Q2: What is the Insphere Radius?
A: The insphere radius is the radius of the largest sphere that can be contained within the polyhedron, touching all its faces.

Q3: Why is this diagonal called "NonSymmetry"?
A: It's called non-symmetry diagonal because it divides the deltoid faces in a way that doesn't follow the main symmetry axes of the polyhedron.

Q4: What are typical applications of this calculation?
A: This calculation is used in geometric modeling, crystallography, architectural design, and mathematical research involving polyhedral structures.

Q5: How accurate is this formula?
A: The formula is mathematically exact for perfect deltoidal icositetrahedrons and provides precise results when correct input values are used.