It forces you to look at the big picture and really think about how you are going to fold this 5 intersecting tetrahedra. Did you know that each seed in a pomegranate is a dodecahedron in nature. The video demonstrates how to fold the six intersecting squares of origami made of modules. I am also wondering where you get all the resources. The units are then assembled to create amazing geometric shapes. I envisioned a book in which each of the twelve chapters or stories represented a face of the dodecahedron. This is an instructional video on how to fold a five intersecting tetrahedra dodecahedron, or more simply, call it a spiky ball. It is one of five regular compounds which can be constructed from identical platonic solids it shares the same vertex arrangement as a regular dodecahedron there are two enantiomorphous forms the same figure but having opposite chirality of this compound polyhedron. The ancients described the platonic solids as the perfect 3 dimensional forms. Hello, up for sale is a beautifully crafted five intersecting tetrahedra origami masterpiece. I made this in real life out of paper see renderings. Figure 3 dodecahedron in the 5 intersecting octahedra matrix.
May you make a instructional video for your five intersecting tetrahedra. Each is the mirror image of the other, and the pair are said to be enantiomorphic. The five intersecting tetrahedra model is based on the dodecahedron. The same thing occurs with their intersections, so that, after isoorientation, the polyhedra intermediate between tetrahedron 4 3m crystallographic point group and icosahedron m 3 5 point group can be compared and their symmetry easily identified. Lustrous, partially gemmy, deep blue some are purplish blue spinel crystals are here found as loose singles and clusters, and also in a scapolitediopsidemica matrix, and, most surprisingly, the crystals are not octahedrons but dodecahedrons, a few of them ideally formed, most of them somewhat distorted. The roman dodecahedrons are also embellished with a serious of knobs on each corner point of pentagons, and the pentagon faces in most cases contain circular holes in them. If you try and print this please post of picture of the result, if it does not work i will edit the file to make the pieces thicker. Begin by using the template below and cutting one face out of each color. Just picture connecting 4 equidistant vertices of a regular dodecahedron. Dodecahedron may be a difficult word to spell, but this 12faced figure is easy to grasp. That is, we need to introduce 2 additional hubs along the octahedrons edges. The compound made from the other five tetrahedra has the swirl in the opposite direction. A dodecahedron has 20 vertices, a tetrahedron has 4, thus you can inscribe 5 seperate intersecting tetrahedra within a dodecahedron where all vertices touchhaha, that was a mouthful. As we mentioned early a picture is really the easiest option.
Dodecahedron in nature pomegranate seeds the smart happy. The two tetrahedra of the compound view of the stellated octahedron are desmic, meaning that when interpreted as a line in projective space each edge of one tetrahedron crosses two opposite edges of the other tetrahedron. It is one of five regular compounds, and dual to the compound of five octahedra. You will need 5 colors, one for each of the apparent tetrahedra. He believed that the they correspond to the four ancient elements, earth, water, air and fire, as well as the universe. I picked up copies of his books a few years ago, theyre. Dodecahedrons article about dodecahedrons by the free. Oct 06, 2008 yeah, this is an instructional video on how to fold the spikeyball.
Concrete necklace which is perfect for your modern minimal outfit. Origami five intersecting tetrahedra complete assembly. Watch this video origami tutorial and learn how to make a modular origami tetrahedra dodecahedron spiky ball. Perry oe 14 dodecahedron 2012 mrhughes student instructions and checkpoints put a v in the box when you have completed an activity. Origami 5 intersecting tetrahedra tetrahedron tutorial. In order to build this model, we need to divide the octahedrons edges into 3 segments. In geometry, a tetrahedrally diminished dodecahedron also tetrahedrally stellated icosahedron or propello tetrahedron is a topologically selfdual polyhedron made of 16 vertices, 30 edges, and 16 faces 4 equilateral triangles and 12 identical quadrilaterals. How to fold an origami star with five intersecting tetrahedra. How to create a tetrahedra origami with five intersections. May 15, 2015 dodecahedron with 5 tetrahedra greg egan this image by greg egan shows 5 ways to inscribe a regular tetrahedron in a regular dodecahedron. How to fold a five intersecting tetrahedra dodecahedron. Since the dodecahedron has 20 vertices, we can inscribe 5 such tetrahedra inside the dodecahedron. Thus the left hand picture illustrates what five intersecting tetrahedra look like, and notice how all these pyramids are cutting into each other.
Free dodecahedron book report idea template, photo of an example, project guidelines, and grade sheet are all available here, for free. If two regular tetrahedra are given the same orientation on the 3fold axis, a different compound is made, with d 3h, 3,2 symmetry, order 12. It helps readers see how origami intersects a variety of mathematical topics, from the more obvious realm of geometry to the fields of algebra, number theory, and combinatorics. Jan 01, 1970 the twinned passions of dodeca and hedron, told in a lighthanded minimalism that belies the sheer virulence. I was inspired to make this by udumplingboi95s recent post. Jun 08, 2014 posts about five intersecting tetrahedra written by franck ramaharo. Jan 31, 2012 howto fold a five intersecting tetrahedra dodecahedron. It has 12 faces, 20 vertices, 30 edges, and 160 diagonals. A few studies have led to the suggestion that these crystal habits can be correlated with chemical compositioni. So the first step would be to make tetras with 72angles 3605 and to tile them into two sets of five tetrahedra to form the top and bottom of the icosahedron, and then i would have to fill the middle area with 10 tetrahedra. This compound was first described by edmund hess in 1876. Howto fold a five intersecting tetrahedra dodecahedron origami fish easy origami cube origami paper folding origami lamp origami envelope origami butterfly modular origami useful origami diy origami when you see one it just makes you stare at it for hours. Rotating star tetrahedra, polyhedra animations and ray traced images rotating star tetrahedra ray traced animations these animations of rotating star tetrahedra are examples of sacred geometry in motion. Other orientations can be chosen as 2 tetrahedra within the compound of five tetrahedra and compound of ten tetrahedral the latter of which can be seen as a hexagrammic pyramid.
It can be seen as a faceting of a regular dodecahedron it is one of the stellations of the rhombic triacontahedron. A dodecahedron s faces are pentagonal, each a five sided polygon. Oct 15, 2014 we are looking for the dodecahedron in nature. The structure is created by combining 5 tetrahedra into one unit within a dodecahedron shape.
I actually did this model i think 10 years ago or so for a friend as a birthday present. Howto fold a five intersecting tetrahedra dodecahedron. This compound polyhedron is also a stellation of the regular icosahedron. It consists of 5 tetrahedrons all connected into a dodecahedron. The template is below for making two intersecting tetrahedron. Dodecahedron article about dodecahedron by the free dictionary. Lets explore the formulas for surface area and volume of the dodecahedron. This tetrahedron has 4 corners, and the dodecahedron has 20 corners total. Complete tutorial showing how to make an origami five intersecting tetrahedra. In fact, five is the minimum number of tetrahedra required to compose a cube.
It might also be visualized as two intersecting tetrahedra. A dodecahedron is a 3d shape that is made of 12 flat faces. Five cubes fit within, with their edges as diagonals of the regular dodecahedron s faces, and together these make up the regular polyhedral compound of five cubes. Intersecting tetrahedra mathematical origami mathigon. Free dodecahedron book report idea template, photo of an. Heavily frontloaded, the first couple sections are completely perfect but by the end the story seems more or less to be running out its prescribed motions with diminishing interest and complexity until it dissipates entirely into the emptiness of the uncaring universe. To see this, starting from a base tetrahedron with 4 vertices, each added tetrahedra adds at most 1 new vertex, so at least 4 more must be added to make a cube, which has 8 vertices. Check out this idea, and lots more at book projects. Five tetrahedrons in a dodecahedron mikes math page.
When you see one it just makes you stare at it for hours. If we were to take 4 equidistant corners of the dodecahedron and connect them with lines, the result would be a pyramid a tetrahedron inscribed in the. I was inspired to make this by udumplingboi95s recent. The arbitrary constraints i put on myself while writing a frame for frames emerge from the geometry of a dodecahedron.
Some of the roman dodecahedrons are basic in design, some have patterns and markings on them. Five intersecting tetrahedra franck ramaharos blog. Dodecahedron with 5 tetrahedra greg egan this image by greg egan shows 5 ways to inscribe a regular tetrahedron in a regular dodecahedron. Jan 26, 2010 complete tutorial showing how to make an origami five intersecting tetrahedra. Decimals dodecahedron project by math tech connections tpt. Seeing the first link made me wonder if we could make the shape out of our zometool set. You can see the yellow tetrahedra almost completely. This is of a nice complex 5 intersecting tetrahedra. A model of 5 interlocking tetrahedra made in catia.
Simple geometry calculator which is used for finding the surface area using edge value of a dodecahedron. Thus we could inscribe 5 distinct tetrahedra inside a dodecahedron. A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of twelve regular pentagonal faces, three meeting at each vertex. Yeah, this is an instructional video on how to fold the spikeyball. The compound of five tetrahedra is one of the five regular polyhedral compounds. There are many different types of dodecahedra, but the one we usually think of is made using 12 pentagons. Making a 5 intersecting tetrahedra with color papers background music. Howto fold a five intersecting tetrahedra dodecahedron 1.
Tetrahedron cube octahedron dodecahedron icosahedron etsy. How to make a model of five intersecting tetrahedra. If you inscribe five, one at each vertex of the topmost face, you create a beautiful solid. The compound of five cubes is one of the five regular polyhedral compounds. Howto fold a five intersecting tetrahedra dodecahedron 1 youtube. More precisely, it shows 5 ways to choose 4 vertices of the dodecahedron that are also vertices of a regular tetrahedron. Leslie gave her great dodecahedron some extra visuals. The roman dodecahedrons ancient roman dodecahedron. This is modeled after the origami 5 intersecting tetrahedron. A cube is a polyhedron bounded by six polygons in this case squares meeting at right angles.
These form the 4 vertices of a regular tetrahedron, as shown on the right figure from tom. Five full tetrahedra will fit inside a dodecahedron in this way. Intersecting dodecahedra mathematical origami mathigon. A year ago, i folded the five intersecting tetrahedra with decent results. Five intersecting tetrahedra dollar origami geometrical etsy. All youll need for this modular origami project is ten sheets of paper in five colors and a lot of patience. By using two colors to create the figure you can make your polyhedron look like two tetrahedra that pass through each other. The dodecahedron has 20 points that it shares with 5 tetrahedra. How to draw dodecahedron the 5 platonic solids youtube. A compound of two spherical tetrahedra can be constructed, as illustrated.
It can be seen as a faceting of a regular dodecahedron. Together, the octahedron and tetrahedron pack space, but neither of them can do so alone. How to make origami 5 intersecting tetrahedra youtube. It is known that the dodecahedron vertices also define 5 cubes and 10 tetrahedra. The small and great stellated dodecahedron have nonconvex regular pentagram faces.
Fun fact i discovered while making it, 5 intersecting tetrahedra make a dodecahedron. This one of the five classic regular polyhedra consisting of 12 pentagonal faces and 20 vertices. May 16, 2015 saw two different references to tetrahedrons in a dodecahedron yesterday. Review decimals with this fun dodecahedron project. If youve already mastered the art of onesheet origami projects like frogs and cranes, challenge yourself to this project. Each pattern makes one pyramidal point of one tetrahedron. This is an advanced modular origami design and an amazing looking paper design. Take 4 vertices in the dodecahedron which are the same distance apart. How to fold a five intersecting tetrahedra dodecahedron origami.
Activities for exploring mathematics, second edition presents a flexible, discoverybased approach to learning origamimath topics. Five intersecting tetrahedra fit was created by thomas hull. One of my favorite mathematical models is the five intersecting tetrhadra model. Within the book, hull provides instructions for one of his most famous models the five intersecting tetrahedra. Compound of five tetrahedra wikimili, the free encyclopedia. Decahedron definition of decahedron by the free dictionary. This is made by creating a 12sided polygon dodecahedron and connecting all the vertices. Tetrahydra modulares origami tutorial video 54 new ideas origami tutorial modular fun a really cool type of modular origami. I am the club president of the origami club in my school and i think the beauty of this origami work will brainwash students to sign up for our club. Hulls book is full of origami and mathematical projects, spanning a variety of mathematical topics including geometry, calculus, graph theory, etc. In total you will be cutting 4 faces of each of the 5 colors. The greek philosopher plato discovered that there are only five solids with these properties.
We have seen how it is possible to inscribe a cube inside a dodecahedron, and also how it is possible to inscribe two tetrahedra inside a cube. With this guide, youll learn how to make a 3d star with five intersecting tetrahedra using origami, the traditional japanese folk art of paper folding. If we choose just one of the inscribed tetrahedra from each cube in a consistent way, we get this very pretty compound of five tetrahedra. Designed by thomas hull presented here by jo nakashima with permission of the. It can be constructed by arranging five tetrahedra in rotational icosahedral symmetry i, as colored in the upper right model. The above embedding divides the cube into five tetrahedra, one of which is regular. A pomegranate is mostly seeds, packed tightly under the skin. All surrounded in a juicy bag of sweetness, but what is interesting is the way they stack. If you would like to make each tetrahedron a unique color, cut four template pieces out of. Origami purists will argue that all origami creations, no matter how complex, should be folded from one single sheet of paper, but the rules were made to be broken, right. Since two tetrahedra can fit on alternate cube vertices, five and ten tetrahedra can also fit in a regular dodecahedron. Howto fold a five intersecting tetrahedra dodecahedron diy.
Being that i had very little experience with origami at the time, i think i racked my brain for a while when it came to the assembly part, but i think i finished it working at it off and on over the. Second in section 327 of henry segermans new 3d printing book linked by evelyn lamb. Modular origami is a type of origami where two or more sheets of paper are folded into units, modules. In this tutorial i used 30 sheets of 5x15cm paper and a small piece of paper as a note. Lauren made a pastel rendition of 5 intersecting tetrahedra. Watch this video origami tutorial and learn how to make a modular origami tetrahe. Rotating star tetrahedra, polyhedra animations and ray. Note each tetrahedron shares one point with the top pentagon, one with the bottom pentagon, and two with the zigzag of ten points around the middle of the dodecahedron. For more information, including a stepbystep overview of the folding process, as well as to get started making your own paper aweinspiring paper stars, watch this free origami lesson.