Midsphere Radius of Deltoidal Icositetrahedron Given Short Edge Calculator

Formula Used:

\[ r_m = \frac{1+\sqrt{2}}{2} \times \frac{7 \times l_e(Short)}{4+\sqrt{2}} \]

Midsphere Radius of Deltoidal Icositetrahedron:

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1. What is the Midsphere Radius of Deltoidal Icositetrahedron?

The Midsphere Radius of a Deltoidal Icositetrahedron is the radius of the sphere that is tangent to all the edges of the Deltoidal Icositetrahedron. It represents the sphere that fits perfectly within the polyhedron, touching each edge at exactly one point.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_m = \frac{1+\sqrt{2}}{2} \times \frac{7 \times l_e(Short)}{4+\sqrt{2}} \]

Where:

\( r_m \) — Midsphere Radius of Deltoidal Icositetrahedron (m)
\( l_e(Short) \) — Short Edge of Deltoidal Icositetrahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the midsphere radius based on the length of the short edge of the deltoidal faces, using the mathematical constant √2.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the spatial properties of the Deltoidal Icositetrahedron. It helps in determining the sphere that can be inscribed within the polyhedron while being tangent to all its edges.

4. Using the Calculator

Tips: Enter the length of the short edge of the Deltoidal Icositetrahedron in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

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

Q2: What is the significance of the midsphere?
A: The midsphere (or intersphere) is a sphere that is tangent to all edges of a polyhedron. It lies between the insphere (tangent to faces) and circumsphere (passing through vertices).

Q3: Are there other ways to calculate the midsphere radius?
A: Yes, the midsphere radius can also be calculated using other parameters of the Deltoidal Icositetrahedron, such as the long edge or surface area, but this calculator uses the short edge for computation.

Q4: What units should I use for input?
A: The calculator uses meters as the unit of measurement. If you have measurements in other units, convert them to meters before input.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the given formula. The result is rounded to 6 decimal places for practical use.