There are 42 NRICH Mathematical resources connected to 2D representations of 3D shapes, you may find related items under 3D geometry, shape and space.
Broad Topics > 3D geometry, shape and space > 2D representations of 3D shapes
Can you find out which 3D shape your partner has chosen before they work out your shape?
The challenge for you is to make a string of six (or more!) graded cubes.
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
Nicola has lost a piece of her 3D jigsaw. Can you work out the shape of the missing piece?
Which faces are opposite each other when this net is folded into a cube?
The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Can you make a new type of fair die with 14 faces by shaving the corners off a cube?
Consider these weird universes and ways in which the stick man can shoot the robot in the back.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
How many different colours would be needed to colour these different patterns on a torus?
How can you represent the curvature of a cylinder on a flat piece of paper?
A task which depends on members of the group working collaboratively to reach a single goal.
A task which depends on members of the group working collaboratively to reach a single goal.
Can you find ways of joining cubes together so that 28 faces are visible?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Put your visualisation skills to the test by seeing which of these molecules can be rotated onto each other.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.
This article, written for teachers, looks at the different kinds of recordings encountered in Primary Mathematics lessons and the importance of not jumping to conclusions!
Some simple ideas about graph theory with a discussion of a proof of Euler's formula relating the numbers of vertces, edges and faces of a graph.
This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.
This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the work of Piaget and Inhelder.
How can we as teachers begin to introduce 3D ideas to young children? Where do they start? How can we lay the foundations for a later enthusiasm for working in three dimensions?
This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.
Can you make a 3x3 cube with these shapes made from small cubes?
Find all the ways to cut out a 'net' of six squares that can be folded into a cube.
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
Can you mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?
In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?