Make yourself a posy of polyhedral tulips
To make this model you will need:
- A printer
- Some method of cutting out paper or thin card
- Quick-drying paper glue
- thread for tying the model to the tree
- Or an Acrobat PDF reader
Download the zipped Drawfiles
(download size 31K) or as PDF
download size 36K. Then follow the directions below to make the model on the
The Draw files (PDF pages) needed to make a copy of the 'Tulips' on show on
the Fortran Friends stand at Wakefield 2001 are in this zipped directory
||the petals of the Tetrahemihexahedron (A) plus
the cream triangles of the pentagonal cupola base|
||the outer triangles of the Tetrahemihexahedron (A) plus
the red parts of the pentagonal cupola base|
||the petals of the Octahemioctahedron (B) and the
Cubohemioctahedron (C) (you need two of these)|
||the petals of the Small icosihemidodecahedron (D) and the
Small dodecahemidodecahedron (E) (you need two of these)|
||the outer parts of the models:|
B (8 large triangles)
C (6 squares)
D (20 small triangles)
E (12 pentagons)
||the bottom of the stand (half a decagonal antiprism)
with half the sides|
||the top of the stand with the other half of the sides
(half a decagonal antiprism with a big hole in it)|
The Draw file 'TulipPlan' (page 1 of the PDF) shows the final object and the
three 'flower' types without their outer parts so that you can see how they
fit together. Print this out so you can follow it easily while you make up
Print the sheets to be cut out on the thickest coloured paper which your
printer will allow. We used 160 gm paper for the models on show at
Start with the simplest model A.
To construct this model (and the pentagonal cupola base) you will need to
print the files 'Base+A1' (we used cream paper for this) and 'Base+A2'
(red) [pages 2 and 3].
Carefully cut round the 7 pieces at the top of 'Base+A1' which are going
to make the petals of this model. Note that each piece has tabs on all its
Score only along the lines which make the tabs; the internal lines are
only for reference and should NOT be scored.
Fold the tabs all the same way on the 4 simple triangular pieces. (We find
that if you fold them towards the inked line, the ink makes less mess of the
On the two pieces with two triangles, fold the two tabs on one triangle up
and the two on the other triangle down.
On the last piece with 4 triangles fold the tabs up and down alternately.
Follow the diagram to glue one of the pieces with two triangles to the one
with four. Make sure that the two tabs on each half of the 2-triangle piece
face the same way as the tabs on the 4-triangle piece. The tabs which are
going to join these petals to the triangular outer parts are shown
transparent only for the top left part of this diagram. The others have been
omitted for clarity.
Next glue in one of the single triangle pieces to support the 2-triangle
piece as shown for the top-left octant of this model. The three external
tabs should all be facing the same way so that the outer red triangle can be
glued straight onto them.
Turn the model round and glue on another 1-triangle piece in exactly the
Turn the model over. This face of the 4-triangle piece has not got lines
on it to guide you but glue the other 2-triangle piece and the two
1-triangle pieces on it in the same way using the petals on the other side
to show you their positions.
Finally glue on the four red outer triangles from 'Base+A2'.
Put aside the rest of the sheets 'Base+A1' and 'Base+A2' for later.
The Octahemioctahedron and the Hexahemioctahedron
Look at the final models marked B and C in the picture of the bunch. You
should see that the structures of the cream petals are the same; the only
difference between them is that eight red triangles are stuck on one of them
and six squares are stuck on the other. This is why there is only one
diagram showing how to construct the cream petals (centre right).
For B the internal and external tabs must all be inside the triangular
parts (to be covered up by the red outer triangle faces), leaving the open
square faces without any visible tabs. The opposite happens for the model C.
Cut out the pieces from a cream sheet 'PetalsB+C' [page 4] and score only
along the tabs.
Fold the tabs on the 6-triangle piece in alternate directions. On the
3-triangle pieces fold the tab on the central triangle the opposite way to
the other four. On the 2-triangle pieces fold the tabs on one triangle one
way and the tabs on the other the other way. The tabs on the single
triangles should all be folded the same way.
The principle of gluing these models is the same as for model A but you
must always be thinking of which way the tabs are supposed to go.
Glue the 3-triangle piece to the 6-triangle piece and support it with two
single triangles as shown on the upper right of the diagram.
Glue a 2-triangle piece between the 3- and 6- pieces and support this
each way with 1-triangle pieces as shown on the top back of the diagram.
Turn it over and do the same again on the other side of the 6-triangle
Finally glue on the 8 large red triangles (or 6 squares) from 'OuterBCDE'
The Small icosihemidodecahedron and the Small dodecahemidodecahedron
Model D (with 20 external triangles) and model E (with 12 external
pentagons) are a similar pair of models. The cream petals are the same for
both except that the tabs face the opposite ways.
Cut out the pieces from a cream sheet 'PetalsD+E' [page 5] and score only
along the tabs.
Fold the tabs on the 10-triangle piece in alternate directions.
Fold the tabs on all short edges the other multiple-triangle pieces in
alternate directions and the ones on the two long edges in the same
direction as the tabs on the short edges of their triangles.
The tabs on the single triangles should all be folded the same way.
The gluing works the same way as for the previous pair of models. Glue the
5- to the 10- and support it with two single triangles, ensuring that the
tabs point the right way. This is shown in the diagram at the bottom of the
page with the 10- horizontal and the 5- above it and going off to the left.
Next glue a 4- to the other side of the 5-, again ensuring that the tabs
go the right way (if the 4- pieces have tabs pointing the wrong way, don't
fold them back but reflect its position; there are two ways the 4- piece
will fit between the 5- and the 10- and only one will have the right tabs).
Fill up the remaining spaces with 2- pieces and then 1- pieces (shown in the
figure on the top left between the 5- and the 10-).
Turn the model over and do the same again on the other side of the
Finally glue on the 20 red triangles (or 12 pentagons) from 'OuterBCDE'
This completes the flowers.
Now make the base which comes in two parts:
Cut out all the parts and score along the internal lines for folding.
- a pentagonal cupola in red and cream (parts in 'Base+A1' and 'Base+A2')
- a decagonal antiprism ('StandB'& 'StandT')
Obtain 5 plastic drinking straws for the stalks and punch out the holes
(marked as solid black circles) in the pentagonal cupola.
Fold them up and glue the two models. You can stick the two parts together
to form the base when you are sure that the straws go through the holes
It then becomes a gyroelongated pentagonal cupola which is one of the
This finishes the base.
Push a small piece of blu-tac into the middle of one opening on each
flower and gently push a straw into it. Then arrange your flowers in their
Well done! Now it's time for tea.
Click here to download a demo version of the
!PolyNet program used to make these files (size 130K).
Click here to see more models to make
Page last updated 28 January 2014
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