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dodecahedron

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dodecahedron
dodecahedron Geom. (ˌdəʊdɪkəˈhiːdrən) Also 6–9 dodecaedron, 6–8 -um. [a. Gr. δωδεκάεδρον, neuter of δωδεκάεδρος, f. δώδεκα twelve + ἕδρα seat, base, face. Cf. F. dodécaèdre (16th c.).] A solid figure having twelve faces: esp. the regular dodecahedron, see quots. 1570, 1653.1570 Billingsley Euclid xi... Oxford English Dictionary
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Rhombic dodecahedron
Bilinski dodecahedron In 1960 Stanko Bilinski discovered a second rhombic dodecahedron with 12 congruent rhombus faces, the Bilinski dodecahedron. See also Dodecahedron Rhombic triacontahedron Trapezo-rhombic dodecahedron Truncated rhombic dodecahedron 24-cell – 4D analog of rhombic dodecahedron Archimede wikipedia.org
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Robotic dodecahedron searches the deep sea for new species
Jan 17, 2024Brennan Phillips. A robotic dodecahedron can capture fragile deep-sea animals to collect tissues samples and construct three-dimensional scans of the creatures, potentially speeding up the ...
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Snub dodecahedron
The snub dodecahedron has the highest sphericity of all Archimedean solids. Geometric relations The snub dodecahedron can be generated by taking the twelve pentagonal faces of the dodecahedron and pulling them outward so they wikipedia.org
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Symmetry group of the dodecahedron and its subsets > Let $G$ be the symmetry group of the dodecahedron. Indicate subsets of the dodecahedron on which $G$ acts by all possible permutations. I know that $G \simeq A_5 \...
If the question is "find all the subsets $E$ of the dodecahedron such that $G$ acts on $E$ by all permutations" then the only possibility is $E=$ {the
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Parabiaugmented dodecahedron
When pyramids are attached to a dodecahedron in other ways, they may result in an augmented dodecahedron (), a metabiaugmented dodecahedron (), a triaugmented dodecahedron (), or even a pentakis dodecahedron if the faces are made to be irregular. wikipedia.org
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Find opposite face of dodecahedron Can anyone tell which one (A,B,C or D) is the opposite face of the face marked in red in the dodecahedron ? What is the best way to find it? ![dodecahedron](
It is opposite (B); you can find this by marking the faces adjacent to the red face, and then marking the faces adjacent to those; then the remaining face, (B), is opposite the red face.
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Demi dodecahedron - what is it? What is a demi dodecahedron? I have not been able to find the geometry of a demi dodecahedron. From latin, what makes a polygon a demi dodecahedron? Can a demi dodecahedron possibly c...
If you cut a regular dodecahedron in half, it looks to me like you can get 10 or 12 faces easily.
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Minimum and maximum diagonal of a dodecahedron Let $s$ be the edge length of a regular dodecahedron. As a function of $s$, what is the dodecahedron's minimum and maximum diagonal (i.e. cross-section)?
Wikipedia gives the radius of the circumscribed sphere as $\frac{\sqrt{15}+\sqrt{3}}{4}s\approx 1.401s$. Your maximum diameter is twice this. It also gives the radius of the inscribed sphere as $\frac{\sqrt{250+110\sqrt{5}}}{20}s\approx 1.1135s$. Is this whatyou menant by minimum diagonal-it is betw...
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Five Cubes in Dodecahedron I will demonstrate why the group of rotational symmetries of a Dodecahedron is $A_5$. For that, we have to find five nice objects, on which the group of symmetries acts. One object is "Cube...
The faces of the dodecahedron are pentagons, with 5 diagonals. Once you have this, make a sketch of the dodecahedron near a face of the cube.
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Icosahedron and inscribed cube We can inscribe a cube in dodecahedron (see this), where $12$ faces of dodecahedron give the $12$ edges of the cube. !enter image description here Can we inscribe cube in icosahedron?
Dodecahedron and icosahedron are dual to one another. Cube in Dodecahedron in Icosahedron Pictures created using a Cinderella Application created by J. Richter-Gebert.
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Symmetries of a dodecahedron Suppose we want to measure order of the group symmetries of a dodecahedron, and we know that If $G$ is a group and $S$ is a set on which $G$ acts and $s\in S$, then Order of G=(Order of s...
Hint: let $s$ be one of the faces of the dodecahedron. As another check on this, you could choose to let $s$ be one of the _vertices_ of the dodecahedron rather than its faces; you should find the same result
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Coloring dodecahedron I found some months ago that there are the Polya's enumeration theorem to compute number of colorings of dodecahedron. I got interested to find how to show by using only Burnside's lemma that the...
You need to work out what the group of rotations of a dodecahedron is (assuming you are not considering reflections), and find the number of colourings
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Formula for greatest cross section of regular dodecahedron Is there a formula for the area of greatest cross section of a regular dodecahedron? For example, this can be viewed as finding a hole big enough for it to f...
I will furnish an answer based on the assumption that the dodecahedron is intended to pass through a hole which is in a plane perpendicular to a fivefold If you were to rotate the dodecahedron to a different orientation (e.g., along a threefold or twofold axis), the shape of the hole would not only be different
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Please explain how to draw a dodecahedron
hi my name is Patricia I'm an artist and I'm going to show you how to draw a dodecahedron and this shape a dodecahedron is a 3d shape made out of polyhedrons and then that way it will give it some dimension again you can add it a little bit here and there you go there is a dodecahedron enjoy you
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