LEARN THROUGH PLAY
Product Introduction
X GEO is composed of several simple and symmetrical polygons. In addition to planar presentation, it can also be assembled into polyhedrons. It is the geometry that mathematicians have been pondering for thousands of years. In the process of using X GEO, you can learn numbers, quantities, shapes, spaces, structures, aesthetics, etc. Geometry can have a lot of varieties, such as making a regular polygon into a polyhedron with the same pattern on each surface. Plato figured out all the possible combinations. Can you figure it out?
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Kit Contents 1
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10
11
3
4
12
Description
Qty.
1
B-CUBE B-CUBE B-CUBE B-CUBE B-CONVEX
2
880-W10-A1R
6
1
880-W10-A1Y
7
2
880-W10-A1W
2 2
3 4 5
Assembly Tips
A. Connecting X GEO
Item No.
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13
No. 2
5
No.
Description
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B-CONVEX B-TRIANGLE B-CONCAVE
880-W10-A1T
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B-20T GEAR WITH AXLE
880-W10-R1R
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D-EQUILATERAL TRIANGLE
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7
15
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Qty.
Item No.
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No.
Description
Qty.
Item No.
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880-W10-R1Y
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2
12
D-SQUARE D-PENTAGON
20 1210-W10-G1TG
880-W10-S1G
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880-W10-D1G
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D-X GEO CONNECTOR
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1210-W10-B1SK
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880-W85-B1R
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7125-W10-A1SK
1210-W10-A1TK
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C-BASE GRID B-PEG REMOVER
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40
1
7061-W10-B1Y
B. Disassemble a 3D Model
12 1210-W10-E1TP
c. Connecting Frames or Rods
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Equilateral Triangle Let’s start with a triangle!
1
Now assemble three triangles, as big as the original one. Position the new triangles on each side of the original one... and the original triangle reappears, but even bigger! Now go ahead and find out just how big you can make the triangle!
Done
Try adding another triangle to each side of the original. Hey presto! The triangle has grown!
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3
Model 1
Equilateral Triangle In addition to expansion, rotation is another interesting variation. Take a point of the triangle as the center at which to connect other triangles, one by one, in rotation, forming a hexagon.
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3
5
2 Put a triangle on each side of the hexagon to form a lovely snowflake.
4
Done
Model 2
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4
Equilateral Triangle Add geometric shapes to form a new pattern. Try the following ways of playing.
Now, we'll try forming a new pattern with the hexagon we assembled earlier.
You will learn to form beautiful patterns by positioning completed models in a particular way. Try to make a rhombus by assembling two triangles. Next, rotate the rhombus to discover how beautiful it is when seen from different angles! Done
5
Model 3
Done
Model 4
Equilateral Triangle + Square When the same thing appears repeatedly, we can call it -Pattern. Geometric figures are the best way to learn model applications. Patterns are used by many professional designers to create fabrics, carved or floor tiles in different colors and patterns.
Done
Model 5
Done
Model 6
This time we will have a go at making a pattern using squares and triangles – this should be an even greater challenge to your originality. The moment of truth arrives. You are sure to discover your talent for design. Keep trying and give your own endless originality a chance to flow spontaneously from your fingertips!
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Equilateral Triangle Return to the large triangle you earlier conjured out of thin air. This time get ready to make a rice dumpling!
Here is your rice dumpling!
Each of the triangles attached to the large one must be folded upward to form a pyramid. Done
Model 7
1
A cube formed from 4 triangles is called a tetrahedron. It was the symbol of fire in ancient Greece. It’s quite a strain on the imagination to think that a delicious pyramid-shaped rice dumpling is made the same way!
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Tetrahedron: A regular tetrahedron is one in which the four triangles are regular, or “equilateral�, and is one of the Platonic solids.
Equilateral Triangle Check It Out: If you assemble two tetrahedrons, how many faces does the new combined solid have?
The new shape you will assemble has an impressive name: a triangular bipyramid.
Done
Model 8
1
Triangular bipyramid: It is a convex deltahedron, it is not a Platonic solid.
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Equilateral Triangle + Square Guess how many combinations of Tetrahedron you can form with X GEO? You will almost certainly find the three combinations shown above.
A
B
Question: Each of those three combinations can form a cube, but only two of them are identical. Which one is different from the other two?
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9
If we add a square at the bottom of the cube that differs from the other two, it turns into an awe inspiring pyramid.
C
Done
Model 9
Equilateral Triangle + Square The triangle can be enlarged. The same goes for the square. Can you make the pyramid bigger?
A square and triangle enlarged even further form an even bigger pyramid! A bigger pyramid is formed by attaching a large triangle on each side of the enlarged square.
Done
Done
Model 10
Model 11
1
Do you know how many triangles and squares were used to make this huge pyramid?
10
Equilateral Triangle
1 Check It Out: Count the number of surfaces on the pyramid. How many surfaces will it have by connecting the undersides of two pyramids? Observe and describe its features. Done
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Model 12
You should find that the cube has eight surfaces. From whatever angle you look at it, you will notice that each of the surfaces is a triangle. This cube is called an octahedron, which is ancient Greece was the symbol for air. It is a Platonic solid.
Equilateral Triangle Placing it on the table for closer observation, you’ll find it resembles a beautiful box with a lid on the top, a cover underneath, and a body covered by six triangles. Sometimes, viewing an object from different angles leads to new discoveries and conclusions. Now, let’s try the following experiment:
1
2
1
3
×2
Done
×2
2
×3
Done
Model 14
Model 13
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Equilateral Triangle Connect five triangles to form the pattern shown. Make two sets of the pattern. Connect the open ends to form a leaf hat (cone).
1
13
Done
Model 15
2
Ă—2
Let’s make a bigger whirligig.
1
Next, connect the two leaf hats to form a whirligig.
Done
Model 16
Equilateral Triangle Try to make a bigger rice dumpling. Remove the triangle at the center of each surface, and connect more equilateral triangle, turn it into the cube shown on the right.
Does it more like a starry night? Done
Model 17
1
Try to make a more bigger rice dumpling again. Turn it into the cube shown on the right, by truncating each of its angles.
This new cube is called a truncated tetrahedron. Done
Model 18
1
14
Equilateral Triangle + Square Make a beautiful dragonfly according to the following picture!
1
1
Now let’s turn each of the dragonfly wings into a cone. Then connect the two cones to the dragonfly body. What does it become? Done
15
You can create a new whirligig by replacing the center triangle with a square!
Done
Model 20
Model 19
This solid, composed of twenty triangular surfaces, is called an icosahedron which, for the ancient Greeks, represented water. Icosahedron: a polyhedron having 20 faces, where all faces are equilateral triangles.
Square So by now you’re able to recognize this square shape. Using the method you are familiar with, try and find how many X GEO pieces you need to construct the box shown below.
Check It Out: In your head, work out how many of the “plans” above can be folded into a cube.
Done
Model 21
Note that the polyhedron construct has six surfaces and each of them is a square. We usually call this a cube. Its official name is hexahedron, but it’s not used very often nowadays. That was a shape used by the ancient Greeks to represent the element, earth.
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Equilateral Triangle + Square Try to complete the pattern according to the picture shown below.
A cuboctahedron will turn into a beautiful vase when its triangular surface is turned upwards and the triangle is replaced by three square pieces.
1
1
Done
1
2
Done
Model 22
Model 23
Cuboctahedron: a polyhedron with eight triangular faces and six square faces.
How about making a big vase like the one shown below? Done
3 4
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This magnificent polyhedron is called a cuboctahedron. A cube will turn into a truncated octahedron when it is shortened from the middle of each of its edges.
Before combining two models, ensure that the Gigo logo faces outward.
Model 24
Equilateral Triangle + Square By now your basic skills are well developed. Well done! Let’s practice some more. Try to complete the house shown below.
1
Done
Model 25
1
Done
Model 26
Think Try to build a bigger and taller house? For example, a farm corn-loaf as shown below.
1
Done
Model 27
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Equilateral Triangle + Square What's the difference when you change the roof?
Done
Model 28
Done
Model 29
1
1
19
Try to build a model of your ideal house?
Equilateral Triangle + Square Try to complete the pattern according to the picture shown below, and convert into 3D models. Its name is “rhombicuboctahedron�.
1
Done
Model 30
Try to complete the pattern according to the picture shown below, and convert into 3D models. This snub cube on the right is a more complex model.
1
Done
Model 31
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Equilateral Triangle + Square Many of human writing and drawing symbols come from geometric figures that can be traced back to ancient times. In some places they even remain the same today, like the trademark pattern. Try to assemble them with reference to patterns in the following pages.
1
Model 32
Done
Done
21
Before combining two models, ensure that the Gigo logo faces outward.
Model 33
1
Equilateral Triangle + Square 1
Done
Done
Model 34
1
Model 35
Before combining two models, ensure that the Gigo logo faces outward.
22
Equilateral Triangle + Square 1
23
Done
Model 36
Done
Model 37
1
Before combining two models, ensure that the Gigo logo faces outward.
Equilateral Triangle + Square + Pentagon Convex and concave forms are also interesting. Try the patterns shown below. Done
Model 38
Done
Model 39
1
1
Before combining two models, ensure that the Gigo logo faces outward.
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Equilateral Triangle + Square A tetrahedron can be transformed into a beautiful box by using a square as the lid and the bottom, with triangles at the sides.
1
Done
Model 40
1
Done
Model 41
1
Done
1
25
Done
Model 42
Model 43
Equilateral Triangle + Square If you observe a snowflake up close, you will be in awe of its dazzling crystalline facets. Have a look at the ones shown in the instruction manual.
1
1
×2
2
×4
×4
3
Done
3
4
Done
Model 44
Model 45
2 Before combining two models, ensure that the Gigo logo faces outward.
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Equilateral Triangle + Square + Pentagon Try to assemble a polyhedron with reference to picture below.
The dodecahedron was the ancient Greek symbol used to represent the universe. Done
Model 46
Done
Model 47
1
What pattern do you get when you connect a pentagon with a triangle?
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Dodecahedron: A regular dodecahedron is a Platonic solid composed of twelve regular pentagonal faces.
Equilateral Triangle + Square + Pentagon You can obtain different structures by connecting the square to the pentagon. Try the following patterns.
1
Done
Model 48
1
Done
Model 49
1
Done
1
Done
Model 51
Model 50
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Equilateral Triangle + Square + Pentagon In adopting a pentagon as the lid and the bottom, you can obtain even more beautiful patterns by adding more X GEO pieces and inserting triangles in the center.
1
1
29
Done
Done
Model 52
Model 53
Done
Model 54
Done
Model 55
1
1
Equilateral Triangle + Square + Pentagon Try the following patterns:
Done
Model 56
1
Done
Model 57
1
Done
Model 58
1
30
Equilateral Triangle + Square + Pentagon Combination of pillar and tetrahedron:
Done
Model 59
Done
Model 60
4 2
1
1
31
×5
2
×4
×5
×4
3
3
4
Before combining two models, ensure that the Gigo logo faces outward.
Equilateral Triangle + Square + Pentagon Mixed combination of the pentagon:
Done
Model 61
1
1
3
Ă—5
2
Ă—5
5
Done
Model 62
4
Before combining two models, ensure that the Gigo logo faces outward.
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Equilateral Triangle + Square + Pentagon Many works of "ceremonial"architecture, such as a stadium or arena, are derived from geometric forms. Let’s build an arena!
1
2
Ă—5
Done
3
Done
1
33
Before combining two models, ensure that the Gigo logo faces outward.
Model 63
Model 64
Equilateral Triangle + Square + Pentagon Right about now you must be feeling that your creative powers are about to explode! Use them to their fullest!
2
1
Done
4
Model 65
3
1
Done
Before combining two models, ensure that the Gigo logo faces outward.
Model 66
Boat
Lighthouse
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Equilateral Triangle + Square + Pentagon
1
Ă—2
Done
2
Model 67
Beautiful Pentagon Box
1
3
4
Done
Model 68
2
35
Before combining two models, ensure that the Gigo logo faces outward.
Airport Control Tower
Equilateral Triangle + Square + Pentagon Does it look like a Papal Crown?
1 Done
Model 69
3
2
Before combining two models, ensure that the Gigo logo faces outward.
36
Equilateral Triangle + Square + Pentagon 1
Model 70
Done
1
3
Done
Big Vase
Model 71
2
37
Before combining two models, ensure that the Gigo logo faces outward.
King’s Crown
Equilateral Triangle + Square + Pentagon 1
Notice what it looks like. An adorable dinosaur? As long as you have enough X GEO there’s no limit to the magic you can perform.
2
Done
Ă—4
3
4
Model 72
A
B
5
A
B
Before combining two models, ensure that the Gigo logo faces outward.
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Here's How Combine the cube with the X GEO board to create creative 3D stationery cases. Try to assemble them with reference to patterns in the following pages.
2
1
3 4
39
3
Done
Model 73
Note Pad Holder
Here's How 3
2
1
1
4
4
Done
Model 74
Pen Holder
40
Here's How 1 1
1
41
Done
2
Done
2
Model 75
Phone Holder Model 76
Pen Pot
Here's How
2
Done
3
Model 77
2 1
3
Business Card Holder
42
#1404
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MADE IN TAIWAN
© 2020 Genius Toy Taiwan Co., Ltd. ALL RIGHTS RESERVED
R21#1408
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