Assignment Brief.

Option-01

Mid-Term/Mid-Module Assessment.

Detailed Assignment Brief:-

1) Learning Diary.

2) Geometrical analysis of Natural and man-made objects.

2) Freehand orthographic projection and isometric views of 04 objects from their core/respective disciplines.

Type of Submission/Deliverables in A-4/A-3 size in LD with freehand sketches/images/illustrations in only A-3 Size.

Option-2

Mid-Term/Mid-Module Assessment

Detailed Assignment Brief: Type of Submission/Deliverables.

1) Learning Diary.

2) Geometrical analysis of artifact (शिल्पकृति) from the craft sector.

3) Freehand orthographic projection and isometric Views of 04 objects from their core/respective disciplines.

Type of Submission/Deliverables in A-4/A-3 size in LD with freehand sketches/images/illustrations in only A-3 Size.

Net for Truncated Dodecahedron

Net for Truncated Dodecahedron

32 faces (20 triangles, 12 decagons), 60 vertices, 90 edges Icosahedral (2, 3, 5 fold) symmetry.

Method:

This net is made in TWO parts.

1. PART - 1. (Step -1) To draw the required decagon (ten-sided polygon), use any previous method to first draw a pentagon, or as follows (Fig.) 

Step 1

       On horizontal AB draw a circle radius OA. Arc above and below from A and B with radius AB, and connect the intersection points to find the vertical which crosses the circle at C and D. Find the midpoint of OB by drawing arcs from B with radius OB to cross the circle above and below. Join the intersection points to find point E. With compass on E and radius EC draw arc down to cross the horizontal at F. With compass on C and radius CF swing an arc to both sides to give points G and H. Walk this radius round to find the other two points of pentagon CHJKG. Draw lines from each pentagon point through the centre to the circle on the other side to find the rest of the points of the decagon CLHMJDKNGP.

2 (Step - 2) Add further decagons to alternate sides of the first decagon by first drawing arcs from each pair of points on the central decagon in turn with the same radius as that of the central circumcircles (the circle that encircles the decagon) to find the centres of the circumcircles of the surrounding decagons.

3. Then walk the side length round each circle to mark the points of each decagon (see Fig.). 

4. (Step - 3) Tune these points by drawing lines through existing and new points. A selection of checking lines only is shown here (see Fig.)

 Step 3.

5. Step - 4) Add equilateral triangles to the faces shown in (Fig 5.69. step-4).

6. (Step - 5) Add tabs and cut and fold lines as shown. The dotted arrow and tab indicates where the other part of the net joins (Fig 5.70 step-5).

7. PART - 2 (Step - 6) -is identical to the first part, except for the tabs - follow carefully (Fig 5.71 step-6).

8. When both parts are made, cut out along the solid lines: score along the dashed lines. Fold upwards along the scored lines.

9. Glue carefully and progressively (tabs inside) - one or two tabs at a time. Clean up and decorate as you wish.👍

 Illustrations of one half of the net drawn out on card and cut out (top left); the two halves assembled (top right and bottom left); and the model complete (bottom right).

Net for Truncated Icosahedron.

Net for Truncated Icosahedron 

32 faces (12 pentagons, 20 hexagons), 60 vertices, 90 edges, Icosahedral (2, 3, 5-fold) symmetry.

Method:-

This net is made in SIX parts:

1. PART 1. (Step - 1) Having chosen your edge length AB on a horizontal line, construct the central pentagon as follows: draw two circles centred on A then B radius AB Draw the vertical axis through the circle intersections C and D to find O (midpoint of AB). Draw a tangent across the top of the two circles, and from the point where this tangent crosses the vertical draw arcs either side radius OA. This gives upper corners E and F of square AEFB. With centre O and radius OE draw a semicircle to cross the horizontal at G and H. AB has now been extended on either side by a Golden Ratio amount. Now draw arcs from A and B with radius AH (=BG). Where they cross on the vertical axis is the upper point J of our pentagon. The other two points are given where the AH and BG ares cross the first circles at L and K. Our pentagon is AKJLB.

Step 1.

2. (Step - 2) On each side of the pentagon construct a hexagon (see Figure) The arrows in the diagram indicate where further sections of the net will be attached.

Hexagon on a line.

Step - 2

3. PARTS 2-5 (Step - 3) Starting with a hexagon (constructed as before) with the same edge length as used in the first drawing, add to the sides one hexagon and two pentagons as shown (Fig.). The pentagons can be more easily drawn this time (see Figure down right) by using the previously drawn pentagon measure with your compasses the length of the diagonal (AJ in Fig.) and draw an arc from each end of the base line. This gives you the apex of the pentagon. Now adjust your compasses to the edge length, and draw an arc from the end of the base line to cross arcs on either side from the apex to find the other two vertices. Finally, one further hexagon is added to the lefthand pentagon to complete this section of the net.

You will need FOUR of these.

Step - 3

Construction of pentagon using arcs of known measurements.

4. PART - 6. (Step - 4) is similar to the previous ones, but with an extra pentagon on one end (Fig.)

Step.- 4.

5. Add tabs, and cut and score lines, as shown. 

6. Cut out along the solid lines: score along the dashed lines. Fold upwards along the scored lines Glue carefully and progressively (tabs inside) - one of two tabs at a time. Clean up and decorate as you wish.👍

Illustration of the six parts of the net drawn out on card and cut out.

Note:

Until 2006 the official World Cup football was made in the shape of a Truncated Icosahedron.

Illustrations of four of the six parts of the net glued (top left); the figure partially assembled (top right); further assembled (bottom left); and complete (bottom right).

Net for Truncated Cube.

Net for Truncated Cube

14 faces (08 triangles, 06 octagons), 24 vertices, 36 edges Octahedral (02, 03, 04-fold) symmetry (समरूपता).

Method:-

1. (Step - 1) Draw four circles on a horizontal. Construct verticals through each circle center and through each diameter point on the edes of the circles. Draw tangents to the four circle above and below to cross the verticals, forming four touching squares.

Step -1.

2. (Step - 2) To complete the first octagon (left most circle in Figure below) draw a circle through the corners of the surrounding square, and join the four points where the new larger circle crosses the horizontal and vertical axes. Where this (dynamic) square - which is the same size as the first (static) square - overlaps the first square, an octagon is formed.

Step - 2.

3. (Step - 3) Repeat to form octagons around the other three circles. Construct equilateral triangles on the sides shown.

Step -3.

Step -4.

4. (Step - 4) Construct an octagon on the side of each of the two triangles shown. Add the final three equilateral triangles to the top octagon.

Step - 5.

5. (Step 5) Add tabs and mark the cut and fold lines as shown.

6. Cut out along the solid lines: score along the dashed lines. Fold upwards along the scored lines. Glue carefully and progressively (tabs inside) - one or two tabs at a time. Clean up and decorate.👍

 Illustrations of the net drawn out on card and cut out (above) and the model partially assembled (facing page down left).

The Model complete. 👍

Net for Truncated Octahedron.

Net for Truncated Octahedron

14 faces (06 squares, 08 hexagons), 24 vertices, 36 edges. Octahedral (02, 03, 04-fold) symmetry.

Construction drawing

Method:

1. On a long horizontal draw a circle centre O (the diameter of your circle should be just less than one sixth of the width of your sheet). Construct the vertical axis through O to give you points A and B. The rest of the construction is drawn using only the original radius.

2. Draw arcs from A to find C and D; and from B to find E and F. This gives you the first hexagon ADFBEC.

3. A line through DC extended to the left, and an arc from C will find G. Similarly, a line through FE and an arc from E will find H. GCEH is the first square. Find squares AJKD and FMLB in the same way by extending EA, BD; and AF, CB.

 Illustration of the net drawn out on card and cut out.

4. Pairs of arcs from A and C, B and E, D and F will cross to find new centres O², O³ and O4. On each of these new centres draw a circle, and walk the radius round each circle to find the points of the hexagons.

5. Square NQRP is found by extending lines through CD and EF to the right, and drawing arcs from N and P to find Q and R. Centre O5 is found by drawing arcs from Q and R to cross. With this new centre established, the rest of the figure is constructed in the same way as the first half.

6. Add tabs and mark the cut and fold lines as shown.

7. Cut out along the solid lines: score along the dashed lines. Fold upwards along the scored lines.

8. Glue carefully and progressively (tabs inside) - one or two tabs at a time. Clean up and decorate as you wish.👍

Note:-

The net can be drawn in two halves, both identical apart from the tabs. You will also need one additional tab to join the two halves together. The dotted line on Figure between points N and P shows this.

 Illustrations of the model partially assembled (above left and middle); complete (above); and a coloured version (below).

Net for the Truncated Tetrahedron.

Net for the Truncated Tetrahedron: 

08 faces (04 triangles, 04 hexagons), 12 vertices, 18 edges. Tetrahedral (2, 3-fold) symmetry.

Construction drawing

Method.

1. The whole construction is drawn using the same radius throughout. Draw a circle centre O' radius O'A. Mark off points B, C, D, E and F on the circle by walking the radius round. You should come back exactly to A from F Draw arcs from E and F to find G; and from to complete the construction. D and E to find second circle centre O२.

2. Draw second circle from O२ which will pass through points D and E. Walk the radius round the circle to find points H, J, K and L Check that you return exactly to E from L Draw ares from D and H to find M, and from Hand J to find third circle centre O३.

3. Draw third circle centred on O३, and walk radius round as before. Draw arcs as before to find Q, and fourth centre O4.

4. Follow the same process for the fourth circle to complete the construction.

5. Add tabs and mark the cut and fold lines as shown. Cut out along the solid lines: score along the dashed lines. Fold upwards along the scored lines. Glue carefully and progressively (tabs inside)-one or two tabs at a time. Clean up and decorate as you wish.👍

 Illustrations of the net drawn out on card and cut out (top); the model partially assembled and complete (left and middle); and a coloured version (right).

Platonic solids: DODECAHEDRON.

Net for the DODECAHEDRON (The Platonic Solids of Universe (or the heavens)

12 Pentagonal faces, 20 Vertices, 30 edges, Icosahedral (2,3,5 fold) symmetry.

 

Dodecahedron (डोडेकहेड्रॉन) द्वादशफ़लक - A three-dimensional shape having twelve plane faces, in particular a regular solid figure with twelve equal pentagonal faces.

Construction drawing for the first half of the net.

Method:

1. Draw a circle centre O radius OA, and the pentagon CHJKG within as follows: draw any honzontal diameter AB through O, and then the perpendicular vertical axis CD (equal ares above and below from A and B) Find the mid point E of OA (arc radius OA from A to cut circle above and below, and connect), Draw an arc centre E radius FC my cat BA at 1: draw arc centre radius CF to cut circle at G. CG is une side of our pentagon, which can be 'valled ' around the circle with the compasses to find the other points H, J and K. Adjust il necessary so that the five points are equally spaced around the circle.

Construction drawing for the med half of the net. Note that this mast be of the same my as the first half.

 

With some care the whole net can be drawn out as one drawing. This requires same skill in the projection of lines from the first half (on the left within the circle) to ensure accuracy - which is why many will find it easier to make the net in two halves.

The two halves of the net drawn out on card and cut out (top), and glued into dishes (bottom).

2. Draw a pentagram (star) within the pentagon by drawing lines from each point to all the other points (from G to H and J; from C to J and K, etc). In the middle of this pentagram is a smaller pentagon LMNPQ.

3. Draw the diagonals of this inner pentagon and extend them to intersect the main pentagon, creating five similar (same size) pentagons surrounding the inner one.

The two halves joined to complete the  DODECAHEDRON.

4. Mark the cut and fold lines as shown.

5. Add tabs as shown.

6. Make a second net of exactly the same size, but omit the outer tabs.

7. Cut out along the solid lines; score along the dashed lines. Fold upwards along the scored lines.

8. Glue both nets carefully and progressively (tabs inside)—one or two tabs at a time. Make sure the outer tabs are not folded too much, as they need spring to engage with the second half Then glue the outer tabs and join one half to the other.

9. Clean up and decorate as you wish. 👍

Platonic solids: Octahedron & Icosahedron.

 Net  for the Octahedron (The Platonic Solids of Air)

08 triangular faces, 06 Vertices, 12 edges, Octahedral (2,3,4 fold) symmetry.

Construction drawing

Illustrations of the net drawn out on card and cut out.

Illustrations of the net in two stage of assembly, and the model complete (right).

Method:

1. Draw a circle with centre O - (judge the position on the sheet as shown, to allow space for top point E).

2. Draw a long horizontal through the centre of the circle parallel to the bottom edge of the sheet.

3. Along the horizontal, with the same radius, draw 2 more circles with centres B and C, and 02 semicircular arcs (shown dashed) centres A and D.

4. Using circle intersection points, draw out the net as shown on facing page.

5. Add tabs as shown: the cut angle can be obtained with reference to points on the drawing as shown. Judge the width by eye.

6. Cut out along the solid lines: score along the dashed lines. Fold upwards along the scored lines. Glue carefully (tabs inside) starting with tabs marked 1. Clean up and decorate as you wish.

 Net  for the Icosahedron (The Platonic Solids of Water)

20 triangular faces, 12 Vertices, 30 edges, Icosahedral (2,3,5 fold) symmetry.

Icosahedron (आइकोशहीड्रोन) 

Definition of Icosahedron - A solid figure with twenty plane faces, especially equilateral triangular ones.

Construction drawing (A)

Illustrations of the net drawn out on card and cut out. (B)

 Illustrations of the model partially assembled (left) and complete (right). (C)

Method:

1. Draw a circle centre O just in from the edge of the sheet and with a radius no more than one sixth of the width of your sheet (see Figure A).

2. Draw a long horizontal through the centre of the circle parallel to the bottom edge of the sheet.

3. Draw 04 more circles along the horizontal overlapping by half a diameter each time. Draw semicircular arcs at the extremes to left and right (shown dashed).

4. Using circle intersection points draw our the net as shown above.

5. Add tabs as shown using points on the drawing as guides to angle them off.

6. Cut out along the solid lines: score along the dashed lines. Fold upwards along the scored lines. Glue carefully and progressively together (tabs inside). I find it easier to glue one or two tabs at a time, and then pause. Clean up and decorate as you wish.👍

PAPER FOLDS FOR THE PLATONIC SOLIDS (Tetrahedron & Cube)

 

The five platonic solids made in card. 

PAPER FOLDS FOR THE PLATONIC SOLIDS

Before you start:

1. A suitable weight of paper depends on the size of model that you are making 300g/m² (water colour or coloured pastel paper) gives you a very stout model, but achieving neat creases can be difficult. Probably best is heavyweight cartridge paper (200 or 220 g/m), which makes good models, can be nicely creased, and can be painted. You could even use 160 g/m² (suitable for use in photocopiers) as long as the model is not so large that it becomes flimsy I usually use a paper size no bigger than A3 to draw out the nets- using several sheets where the net is drawn out in multiple parts

2. In addition to your straight edge, pencil and compasses, you will find it useful to have two coloured pencils to distinguish between lines to be cut and lines to be scored and folded. If you do not have coloured pencils, distin guish between the two types of lines by using bold solid lines for the 'cut lines, and broken (dashed) lines for the score and fold' lines (as used here throughout in the instruction sheets).

3. You will also need a scalpel or craft knife, a cutting board, and glue (Uhu General Purpose is good).

4. Draw the construction faintly at first, then strengthen the 'cut' and 'fold' lines when you have completed the whole drawing The finished model looks best if you fold your card so that the score lines as well as the drawn construction are inside, and gives you clean surfaces for decoration.

5. If you are not experienced in scoring, practise first to work out how much pressure is needed for the scored line to fold nicely. Score too deeply and your tabs will fall off! With practice, the back of a scalpel blade works well with thick water colour paper, and the back of an old blunt knife works better on thinner card.

Net  for the Tetrahedron (The Platonic Solids of Fire)

04 triangular faces, 04 Vertices, 06 edges, Tetrahedron (2,3-fold) symmetry.

Construction drawing

Illustrations of the net drawn out on card and cut out (left), Part assembled (centre)  and the model complete (right).

Method:

1. Draw a circle centre O - (judge the position on the sheet, allowing space for top point E).

2. By eye, draw a long horizontal through the centre of the circle parallel to the bottom edge of the sheet.

3. Draw 2 arcs with the same radius from the diameter points A and B to intersect the circle above and below. The intersections above will give you points C and D.

4. To find E: either, use your straight edge to extend AC and BD to cross; or, draw arcs from C and D to cross.

5. Add tabs as shown.

6. Cut out along the solid lines: score along the dashed lines.

7. Fold upwards along the scored lines.

8. Glue carefully (tabs inside) starting with tab marked 1.

9. Clean up and decorate as you wish.

Net for the Cube (The Platonic Solid of Earth)

06 square faces, 08 vertices, 12 edges Octahedral (2, 3, 4-fold) symmetry

Construction drawing

Method:

1. Draw a horizontal in the centre of your sheet. Using your compass, mark off four equal measures (points 1, 2, 3, 4 and 5 in Figure above) - with a bit to spare at each end; making sure also that there is room vertically for three measures plus something to spare top and bottom.

2. On points 2 and 3 draw circles with radius the 'measure'.

3. Draw the vertical through the two points where the circles intersect to give the midpoint O, as well as A and B.

Illustration of the net drawn out on card

4. Draw a circle centre O radius 02. Repeat along the horizontal between points 1 and 2, 3 and 4, 4 and 5.

5. Draw horizontal lines tangenting above and below the four circles.

 6. Mark off the corner points of the square about circle O using radius OA from points A and B. Connect the corner points and extend above and below:

7. Setting compass to the original measure, mark off corner points for the rest of the squares required (points C, D, E, E, G, H, J, K, L, M).

8. Add tabs at 45° as shown using diagonals where possible. Judge the width by eye.

9. Cut out along the solid lines score along the dashed lines Fold upwards along the scored lines.

10. Glue carefully and progressively (tabs inside). Clean up and decorate as you wish.

Illustrations of the model partially assembled (abore) and complete (below)

Constructing Small 3D Stick Models

The Five Platonic Solids.

Before you start:

1. You will need: sticks, cutting board, cutting knife (scalpel or craft knife) and glue (I use Studio Gum rubber adhesive). I buy plain round wooden sticks 2 or 2.5 mm in diameter and either 150 or 200 mm long. They can be coloured using water colours. Some craft suppliers offer pre-coloured sticks.

2. It is important to understand how the glue works. Studio Gum works well because it remains flexible for some time after it sticks, so models can be adjusted without falling to pieces. But first the tips of the sticks need to be dipped into the glue and set aside to become tacky - which means you should be able to hold one stick, attach another to the end, and dangle it without it falling off. If it falls off, the glue has not reached the required tackiness. If you try to stick your model together too soon, the glue will not do its job. It is best to work out how many sticks you will need for the particular of part the model you are making, glue up the required sticks, and then set them aside to become tacky. Apply glue to both ends to be joined together.

Tetrahedron

04 triangular races, 04 vertices, 06 edges.

Method :

Required: 06 sticks (all one length) 

1. Make a base triangle using 03 sticks. 

2.Erect a tripod above (03 sticks brought together  at the apex).

Cube (Hexabedron)

6 square faces, 8 vertices, 12 edges.

Method:

Required: 12 sticks (all one length); 6 sticks (all √2 or 1.414 times longer). Measure the short length, then either construct geometrically or use a calculator to work out the longer length.

1. Make a base square reinforced with one √2 diagonal

2. Erect one corner opposite the base diagonal braced by two diagonals.

3. Erect the opposite corner braced again by two diagonals 

4. Complete in turn each remaining corner, comprising one corner post and two sides of the top square (3 sticks each corner). Then add the final diagonal along the top.

Note that the diagonals are in the form of a Tetrahedron.