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1. John Greschak - Dodecahedron
- www.greschak.com
- A dodecahedron has 12 pentagonal faces, 30 edges and 20 vertices. ...
- This image of a dodecahedron was created by Tom Gettys using the program Persistence of Vision. ...
- See also Transparent Dodecahedron, Tetrahedron, Hexahedron, Octahedron, Icosahedron, Platonic Solid .
2. Dodecahedron biography .ms
- dodecahedron.biography.ms
- Dodecahedron.
- Dodecahedron .
- A dodecahedron is a Platonic solid composed of twelve pentagonal faces, with three meeting at each vertex. ... Canonical coordinates for the vertices of a dodecahedron centered at the origin are {(0,±1/φ,±φ), (±1/φ,±φ,0), (±φ,0,±1/φ), (±1,±1,±1)}, where φ = (1+√5)/2 is the golden mean. Five cubes can be made from these, with their edges as diagonals of the dodecahedron's faces, and together these comprise the regular polyhedral compound of five cubes. The stellations of the dodecahedron make up three of the four Kepler-Poinsot solids. ...
- The area A and the volume V of a regular dodecahedron of edge length a are: .
- The term dodecahedron is also used for other polyhedra with twelve faces, most notably the rhombic dodecahedron which is dual to the cuboctahedron and occurs in nature as a crystal form. The normal dodecahedron is sometimes called the pentagonal dodecahedron to distinguish it. ...
- The 20 vertices and 30 edges of a dodecahedron form the basic map for a computer game called Hunt The Wumpus. ...
- Truncated dodecahedron .
3. tetrahedrally ... dodecahedron and icosahedron
- www.ac-noumea.nc
- tetrahedrally truncated dodecahedron and stellated icosahedron.
- If it seems natural that a truncation of the regular dodecahedron leads to a convex polyhedron, it is more surprising for a stellation of the regular icosahedron! These polyhedra with tetrahedral symmetry have been described by George W. ...
- For the dodecahedron we completely truncate (through the three adjacent vertices) four vertices which belong to an inscribed tetrahedron; 4 triangular faces appear and the 12 pentagons are transformed into isosceles trapeziums.
- Remarks : If we perform the first stellation of the icosahedron on four opposite pairs of faces, 8 faces disappear and it remains an equifacial dodecahedron (the faces are symmetric pentagons); thus it is topologically identical to the regular dodecahedron, but with a tetrahedral symmetry (only three planes of symmetry).
- The mineralogist's tetartoid is an other equifacial dodecahedron (the faces are irregular pentagons) topologically identical to the regular dodecahedron with a tetrahedral symmetry (no planes of symmetry).
4. Dodecahedron and Icosahedron
- cage.rug.ac.be
- The regular dodecahedron and icosahedron .
- The regular dodecahedron .
- In Golden section - Pentagon - Dodecahedron I have explained how a regular dodecahedron can be constructed starting from a cube and what relation exists between the edge of this dodecahedron and the edge of the given cube. ...
- The ratio edge of the dodecahedron / edge of the cube is the inverse of the golden number Phi. If we consider also a second cube, "circumscribing" the dodecahedron the ratio of the edge of the dodecahedron and the edge of this second cube is the inverse of the square of Phi. ...
- Relations between dodecahedron and icosahedron .
- A very interesting property about the regular icosahedron and dodecahedron inscribed in the same sphere is expressed in proposition 2: .
- The same circle circumscribes both the pentagon of the dodecahedron and the triangle of the icosahedron inscribed in the same sphere. ...
- From this proposition it follows that the dodecahedron an isosahedron inscribed in the same sphere also share their inscribed sphere. ...
- The dodecahedron and icosahedron as "Dual Polyhedra" .
- The centers of the faces of a regular dodecahedron are the vertices of a regular icosahedron and the centers of the faces of a regular icosahedron are the vertices of a regular dodecahedron. ...
- The centers of the (twenty) faces of this icosahedron are the vertices of a regular dodecahedron. ...
5. Hexagons in a Dodecahedron
- www.drking.plus.com
- - Hexagons in a Dodecahedron -.
- If you'd like to make half a dodecahedron showing this regular hexagon face from paper, there is a net here.
- Cutting the dodecahedron in half another way also reveals a hexagon, this time symmetric but not regular:.
- Not really relevant here at the Hall of Hexagons, but at the heart of a dodecahedron you'll find a cube:.
6. DODECAHEDRON
- www.mi.sanu.ac.yu
7. Dodecahedron
- www.public.asu.edu
- The Dodecahedron.
- The dodecahedron has 12 pentagon faces, 20 vertices, and 30 edges. The dual of the dodecahedron is the icosahedron (by interchanging the number of faces and vertices), with 20 faces, 12 vertices, and 30 edges. ...
- The Gumbo Limbo photos and dodecahedron in darkness photos have extra information in the alt tags about the platonic solids, and natural fractals. ...
- The version on the left is what the camera took, taken before dawn, with the dodecahedron floating in the ocean waves. ... The dodecahedron was barely visible in the water, and maintaining eye contact, I'd hurry up snap a picture as though it were visible in the lens. It was surprizing how many of them came out, even though the dodecahedron was moving with the water. In the far-right image, the flash illuminated a single face of the dodecahedron, and it looks rather eerie. ...
- Two mornings later, I went back to repeat this with all of the inflatables, thinking it would be safe since the dodecahedron hadn't floated away. ...
8. Construction of the Icosahedron and the Dodecahedron
- carp.rutgers.edu
- Construction of the Icosahedron and the Dodecahedron .
9. Dodecahedron
- www.bekkoame.ne.jp
- Dodecahedron .
- If MouseDown outside of dodecahedron, then drag total object. ...
- There are 12 faces in dodecahedron. ...
10. 12hedron
- www.goldenmeangauge.co.uk
- 4 The Dodecahedron.
- The dodecahedron is one of the 5 Platonic solids with 12 pentagonal surfaces.
- The dodecahedron contain 3 Golden Proportion intersecting rectangles, as seen in the adjacent diagram. ...
- The icosahedron fits well as an inscribed solid within the dodecahedron.
11. Roman bronze dodecahedron.
- museums.ncl.ac.uk
- Bronze Dodecahedron.
- The bronze dodecahedron was found during the 19th century excavations of South Shields Roman fort (Arbeia) and bequeathed to the Society of Antiquaries of Newcastle upon Tyne by Robert Blair, a local solicitor who was involved in the work at Arbeia over many years.
- In view of the response we have received to the dodecahedron we have added a bibliography of specialist papers on the subject. ...
12. dodecahedron
- kjmaclean.com
- THE DODECAHEDRON .
- The dodecahedron has 30 edges, 20 vertices and 12 faces. ...
- The dodecahedron is the only polyhedron I know of which is composed entirely of pentagons. ...
- The dodecahedron is pentagonal both inside and out, as can be seen from Figure 1. ...
- The dodecahedron is even more versatile then the icosahedron. ...
- \/¯3 and \/¯5 geometry, but the dodecahedron contains \/¯2, \/¯3, and \/¯5 geometry! .
- Figure 2A -- Another view of tetrahedron (green) inside cube (blue) inside dodecahedron (orange) .
- Figures 2 and 2A show how a cube and a tetrahedron can be placed inside a dodecahedron. These placements are 'nice' meaning that the vertices of the placed-in solids are all vertices of the dodecahedron. ...
- Since the Octahedron can be formed from the tetrahedron by bisecting each of the sides of the tetrahedron (shown below in Figure 3), the dodecahedron can contain the 3 regular solids not based on \/¯5 geometry. ...
- The icosehedron and the dodecahedron are 'duals' (as are the cube and the octahedron). ...
- So by placing a vertex at the middle of all the faces of the dodecahedron you get an icosahedron, and vice-versa. Figure 4 shows the dual nature of the icosahedron and dodecahedron. ...
- What is the volume of the dodecahedron? .
- Imagine a sphere surrounding the dodecahedron and touching all of its vertices .
- In fact, like the icosahedron, the dodecahedron is composed of rectangles divided in Extreme and Mean Ratio. ...
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