Make 3D Shapes

Total Page：16

File Type：pdf, Size：1020Kb

MAKING 3D SHAPES www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Thank you! Thanks for downloading these excellent 3D shape nets from Great Maths Teaching Ideas! Teaching 3D shape topics lends itself to kinaesthetic teaching styles. I have always found that when getting pupils to draw 2D views of 3D shapes, having the 3D shapes for them to hold and manipulate in their hands provides important support for many learners. As well as covering the topic of nets, these resources could then be used to look at other 3D shape topics including surface area, volume and Euler’s famous formula F + V - E = 2. Specifically, getting the pupils to calculate surface area of the net first is a great way to introduce the concept of surface area. Thanks again for downloading these resources and I hope you and your students get lots of quality learning experiences from them! www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Copyright I want these resources to be available to as many teachers and students as want to use them. Hours of work went into the production of these resources and I do need to cover the cost of their production by charging a small fee for them. Purchasing this resource from the www.greatmathsteachingideas.com website entitles the buyer to use and reproduce these resources for educational use with their own classes. If other teachers would like to use these resources please ensure they purchase their own copy from the above website. Thank you. www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Contents Nets Triangular Prism Cube Cuboid Pentagonal Prism Square Based Pyramid Pentagonal Based Pyramid Hexagonal Based Pyramid Tetrahedron Octahedron Dodecahedron Icosahedron Cylinder www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Triangular Prism www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Cube www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Cuboid www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Pentagonal Prism www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Square Based Pyramid www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Pentagonal Based Pyramid www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Hexagonal Based Pyramid www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Tetrahedron www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Octahedron www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Dodecahedron www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Icosahedron www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved Cylinder www.greatmathsteachingideas.com ⓒ 2010 All Rights Reserved www.greatmathsteachingideas.com.

Copy Link

Recommended publications

Name Date Period 1
NAME DATE PERIOD Unit 1, Lesson 13: Polyhedra Let’s investigate polyhedra. 13.1: What are Polyhedra? Here are pictures that represent polyhedra: Here are pictures that do not represent polyhedra: 1. Your teacher will give you some figures or objects. Sort them into polyhedra and non- polyhedra. 2. What features helped you distinguish the polyhedra from the other figures? 13.2: Prisms and Pyramids 1. Here are some polyhedra called prisms. 1 NAME DATE PERIOD Here are some polyhedra called pyramids. a. Look at the prisms. What are their characteristics or features? b. Look at the pyramids. What are their characteristics or features? 2 NAME DATE PERIOD 2. Which of the following nets can be folded into Pyramid P? Select all that apply. 3. Your teacher will give your group a set of polygons and assign a polyhedron. a. Decide which polygons are needed to compose your assigned polyhedron. List the polygons and how many of each are needed. b. Arrange the cut-outs into a net that, if taped and folded, can be assembled into the polyhedron. Sketch the net. If possible, find more than one way to arrange the polygons (show a different net for the same polyhedron). Are you ready for more? What is the smallest number of faces a polyhedron can possibly have? Explain how you know. 13.3: Assembling Polyhedra 1. Your teacher will give you the net of a polyhedron. Cut out the net, and fold it along the edges to assemble a polyhedron. Tape or glue the flaps so that there are no unjoined edges.
[Show full text]
Systematics of Atomic Orbital Hybridization of Coordination Polyhedra: Role of F Orbitals
molecules Article Systematics of Atomic Orbital Hybridization of Coordination Polyhedra: Role of f Orbitals R. Bruce King Department of Chemistry, University of Georgia, Athens, GA 30602, USA; [email protected] Academic Editor: Vito Lippolis Received: 4 June 2020; Accepted: 29 June 2020; Published: 8 July 2020 Abstract: The combination of atomic orbitals to form hybrid orbitals of special symmetries can be related to the individual orbital polynomials. Using this approach, 8-orbital cubic hybridization can be shown to be sp3d3f requiring an f orbital, and 12-orbital hexagonal prismatic hybridization can be shown to be sp3d5f2g requiring a g orbital. The twists to convert a cube to a square antiprism and a hexagonal prism to a hexagonal antiprism eliminate the need for the highest nodality orbitals in the resulting hybrids. A trigonal twist of an Oh octahedron into a D3h trigonal prism can involve a gradual change of the pair of d orbitals in the corresponding sp3d2 hybrids. A similar trigonal twist of an Oh cuboctahedron into a D3h anticuboctahedron can likewise involve a gradual change in the three f orbitals in the corresponding sp3d5f3 hybrids. Keywords: coordination polyhedra; hybridization; atomic orbitals; f-block elements 1. Introduction In a series of papers in the 1990s, the author focused on the most favorable coordination polyhedra for sp3dn hybrids, such as those found in transition metal complexes. Such studies included an investigation of distortions from ideal symmetries in relatively symmetrical systems with molecular orbital degeneracies [1] In the ensuing quarter century, interest in actinide chemistry has generated an increasing interest in the involvement of f orbitals in coordination chemistry [2–7].
[Show full text]
Unit 6 Visualising Solid Shapes(Final)
• 3D shapes/objects are those which do not lie completely in a plane. • 3D objects have different views from different positions. • A solid is a polyhedron if it is made up of only polygonal faces, the faces meet at edges which are line segments and the edges meet at a point called vertex. • Euler’s formula for any polyhedron is, F + V – E = 2 Where F stands for number of faces, V for number of vertices and E for number of edges. • Types of polyhedrons: (a) Convex polyhedron A convex polyhedron is one in which all faces make it convex. e.g. (1) (2) (3) (4) 12/04/18 (1) and (2) are convex polyhedrons whereas (3) and (4) are non convex polyhedron. (b) Regular polyhedra or platonic solids: A polyhedron is regular if its faces are congruent regular polygons and the same number of faces meet at each vertex. For example, a cube is a platonic solid because all six of its faces are congruent squares. There are five such solids– tetrahedron, cube, octahedron, dodecahedron and icosahedron. e.g. • A prism is a polyhedron whose bottom and top faces (known as bases) are congruent polygons and faces known as lateral faces are parallelograms (when the side faces are rectangles, the shape is known as right prism). • A pyramid is a polyhedron whose base is a polygon and lateral faces are triangles. • A map depicts the location of a particular object/place in relation to other objects/places. The front, top and side of a figure are shown. Use centimetre cubes to build the figure.
[Show full text]
2D and 3D Shapes.Pdf
& • Anchor 2 - D Charts • Flash Cards 3 - D • Shape Books • Practice Pages rd Shapesfor 3 Grade by Carrie Lutz T hank you for purchasing!!! Check out my store: http://www.teacherspayteachers.com/Store/Carrie-Lutz-6 Follow me for notifications of freebies, sales and new arrivals! Visit my BLOG for more Free Stuff! Read My Blog Post about Teaching 3 Dimensional Figures Correctly Credits: Carrie Lutz©2016 2D Shape Bank 3D Shape Bank 3 Sided 5 Sided Prisms triangular prism cube rectangular prism triangle pentagon 4 Sided rectangle square pentagonal prism hexagonal prism octagonal prism Pyramids rhombus trapezoid 6 Sided 8 Sided rectangular square triangular pyramid pyramid pyramid Carrie LutzCarrie CarrieLutz pentagonal hexagonal © hexagon octagon © 2016 pyramid pyramid 2016 Curved Shapes CURVED SOLIDS oval circle sphere cone cylinder Carrie Lutz©2016 Carrie Lutz©2016 Name _____________________ Side Sort Date _____________________ Cut out the shapes below and glue them in the correct column. More than 4 Less than 4 Exactly 4 Carrie Lutz©2016 Name _____________________ Name the Shapes Date _____________________ 1. Name the Shape. 2. Name the Shape. 3. Name the Shape. ____________________________________ ____________________________________ ____________________________________ 4. Name the Shape. 5. Name the Shape. 6. Name the Shape. ____________________________________ ____________________________________ ____________________________________ 4. Name the Shape. 5. Name the Shape. 6. Name the Shape. ____________________________________ ____________________________________ ____________________________________ octagon circle square rhombus triangle hexagon pentagon rectangle trapezoid Carrie Lutz©2016 Faces, Edges, Vertices Name _____________________ and Date _____________________ 1. Name the Shape. 2. Name the Shape. 3. Name the Shape. ____________________________________ ____________________________________ ____________________________________ _____ faces _____ faces _____ faces _____Edges _____Edges _____Edges _____Vertices _____Vertices _____Vertices 4.
[Show full text]
Lesson 23: the Volume of a Right Prism
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 23 7•3 Lesson 23: The Volume of a Right Prism Student Outcomes . Students use the known formula for the volume of a right rectangular prism (length × width × height). Students understand the volume of a right prism to be the area of the base times the height. Students compute volumes of right prisms involving fractional values for length. Lesson Notes Students extend their knowledge of obtaining volumes of right rectangular prisms via dimensional measurements to understand how to calculate the volumes of other right prisms. This concept will later be extended to finding the volumes of liquids in right prism-shaped containers and extended again (in Module 6) to finding the volumes of irregular solids using displacement of liquids in containers. The Problem Set scaffolds in the use of equations to calculate unknown dimensions. Classwork Opening Exercise (5 minutes) Opening Exercise The volume of a solid is a quantity given by the number of unit cubes needed to fill the solid. Most solids—rocks, baseballs, people—cannot be filled with unit cubes or assembled from cubes. Yet such solids still have volume. Fortunately, we do not need to assemble solids from unit cubes in order to calculate their volume. One of the first interesting examples of a solid that cannot be assembled from cubes, but whose volume can still be calculated from a formula, is a right triangular prism. What is the area of the square pictured on the right? Explain. The area of the square is ퟑퟔ 퐮퐧퐢퐭퐬ퟐ because the region is filled with ퟑퟔ square regions that are ퟏ 퐮퐧퐢퐭 by ퟏ 퐮퐧퐢퐭, or ퟏ 퐮퐧퐢퐭ퟐ.
[Show full text]
Convex Polytopes and Tilings with Few Flag Orbits
Convex Polytopes and Tilings with Few Flag Orbits by Nicholas Matteo B.A. in Mathematics, Miami University M.A. in Mathematics, Miami University A dissertation submitted to The Faculty of the College of Science of Northeastern University in partial fulfillment of the requirements for the degree of Doctor of Philosophy April 14, 2015 Dissertation directed by Egon Schulte Professor of Mathematics Abstract of Dissertation The amount of symmetry possessed by a convex polytope, or a tiling by convex polytopes, is reflected by the number of orbits of its flags under the action of the Euclidean isometries preserving the polytope. The convex polytopes with only one flag orbit have been classified since the work of Schläfli in the 19th century. In this dissertation, convex polytopes with up to three flag orbits are classified. Two-orbit convex polytopes exist only in two or three dimensions, and the only ones whose combinatorial automorphism group is also two-orbit are the cuboctahedron, the icosidodecahedron, the rhombic dodecahedron, and the rhombic triacontahedron. Two-orbit face-to-face tilings by convex polytopes exist on E1, E2, and E3; the only ones which are also combinatorially two-orbit are the trihexagonal plane tiling, the rhombille plane tiling, the tetrahedral-octahedral honeycomb, and the rhombic dodecahedral honeycomb. Moreover, any combinatorially two-orbit convex polytope or tiling is isomorphic to one on the above list. Three-orbit convex polytopes exist in two through eight dimensions. There are infinitely many in three dimensions, including prisms over regular polygons, truncated Platonic solids, and their dual bipyramids and Kleetopes. There are infinitely many in four dimensions, comprising the rectified regular 4-polytopes, the p; p-duoprisms, the bitruncated 4-simplex, the bitruncated 24-cell, and their duals.
[Show full text]
Step 1: 3D Shapes
Year 1 – Autumn Block 3 – Shape Step 1: 3D Shapes © Classroom Secrets Limited 2018 Introduction Match the shape to its correct name. A. B. C. D. E. cylinder square- cuboid cube sphere based pyramid © Classroom Secrets Limited 2018 Introduction Match the shape to its correct name. A. B. C. D. E. cube sphere square- cylinder cuboid based pyramid © Classroom Secrets Limited 2018 Varied Fluency 1 True or false? The shape below is a cone. © Classroom Secrets Limited 2018 Varied Fluency 1 True or false? The shape below is a cone. False, the shape is a triangular-based pyramid. © Classroom Secrets Limited 2018 Varied Fluency 2 Circle the correct name of the shape below. cylinder pyramid cuboid © Classroom Secrets Limited 2018 Varied Fluency 2 Circle the correct name of the shape below. cylinder pyramid cuboid © Classroom Secrets Limited 2018 Varied Fluency 3 Which shape is the odd one out? © Classroom Secrets Limited 2018 Varied Fluency 3 Which shape is the odd one out? The cuboid is the odd one out because the other shapes are cylinders. © Classroom Secrets Limited 2018 Varied Fluency 4 Follow the path of the cuboids to make it through the maze. Start © Classroom Secrets Limited 2018 Varied Fluency 4 Follow the path of the cuboids to make it through the maze. Start © Classroom Secrets Limited 2018 Reasoning 1 The shapes below are labelled. Spot the mistake. A. B. C. cone cuboid cube Explain your answer. © Classroom Secrets Limited 2018 Reasoning 1 The shapes below are labelled. Spot the mistake. A. B. C. cone cuboid cube Explain your answer.
[Show full text]
[ENTRY POLYHEDRA] Authors: Oliver Knill: December 2000 Source: Translated Into This Format from Data Given In
ENTRY POLYHEDRA [ENTRY POLYHEDRA] Authors: Oliver Knill: December 2000 Source: Translated into this format from data given in http://netlib.bell-labs.com/netlib tetrahedron The [tetrahedron] is a polyhedron with 4 vertices and 4 faces. The dual polyhedron is called tetrahedron. cube The [cube] is a polyhedron with 8 vertices and 6 faces. The dual polyhedron is called octahedron. hexahedron The [hexahedron] is a polyhedron with 8 vertices and 6 faces. The dual polyhedron is called octahedron. octahedron The [octahedron] is a polyhedron with 6 vertices and 8 faces. The dual polyhedron is called cube. dodecahedron The [dodecahedron] is a polyhedron with 20 vertices and 12 faces. The dual polyhedron is called icosahedron. icosahedron The [icosahedron] is a polyhedron with 12 vertices and 20 faces. The dual polyhedron is called dodecahedron. small stellated dodecahedron The [small stellated dodecahedron] is a polyhedron with 12 vertices and 12 faces. The dual polyhedron is called great dodecahedron. great dodecahedron The [great dodecahedron] is a polyhedron with 12 vertices and 12 faces. The dual polyhedron is called small stellated dodecahedron. great stellated dodecahedron The [great stellated dodecahedron] is a polyhedron with 20 vertices and 12 faces. The dual polyhedron is called great icosahedron. great icosahedron The [great icosahedron] is a polyhedron with 12 vertices and 20 faces. The dual polyhedron is called great stellated dodecahedron. truncated tetrahedron The [truncated tetrahedron] is a polyhedron with 12 vertices and 8 faces. The dual polyhedron is called triakis tetrahedron. cuboctahedron The [cuboctahedron] is a polyhedron with 12 vertices and 14 faces. The dual polyhedron is called rhombic dodecahedron.
[Show full text]
A Method for Predicting Multivariate Random Loads and a Discrete Approximation of the Multidimensional Design Load Envelope
International Forum on Aeroelasticity and Structural Dynamics IFASD 2017 25-28 June 2017 Como, Italy A METHOD FOR PREDICTING MULTIVARIATE RANDOM LOADS AND A DISCRETE APPROXIMATION OF THE MULTIDIMENSIONAL DESIGN LOAD ENVELOPE Carlo Aquilini1 and Daniele Parisse1 1Airbus Defence and Space GmbH Rechliner Str., 85077 Manching, Germany [email protected] Keywords: aeroelasticity, buffeting, combined random loads, multidimensional design load envelope, IFASD-2017 Abstract: Random loads are of greatest concern during the design phase of new aircraft. They can either result from a stationary Gaussian process, such as continuous turbulence, or from a random process, such as buffet. Buffet phenomena are especially relevant for fighters flying in the transonic regime at high angles of attack or when the turbulent, separated air flow induces fluctuating pressures on structures like wing surfaces, horizontal tail planes, vertical tail planes, airbrakes, flaps or landing gear doors. In this paper a method is presented for predicting n-dimensional combined loads in the presence of massively separated flows. This method can be used both early in the design process, when only numerical data are available, and later, when test data measurements have been performed. Moreover, the two-dimensional load envelope for combined load cases and its discretization, which are well documented in the literature, are generalized to n dimensions, n ≥ 3. 1 INTRODUCTION The main objectives of this paper are: 1. To derive a method for predicting multivariate loads (but also displacements, velocities and accelerations in terms of auto- and cross-power spectra, [1, pp. 319-320]) for aircraft, or parts of them, subjected to a random excitation.
[Show full text]
Optimization of Tensegrity Lattice with Truncated Octahedral Units
OptimizationM. Ohsaki, J. Y. of Zhang, tensegrity K. Kogiso lattice andwith J. truncated J. Rimoli octahedral units Proceedings of the IASS Annual Symposium 2019 – Structural Membranes 2019 Form and Force 7 – 10 October 2019, Barcelona, Spain C. Lázaro, K.-U. Bletzinger, E. Oñate (eds.) Optimization of tensegrity lattice with truncated octahedral units Makoto OHSAKI∗a, Jingyao ZHANGa, Kosuke KOGISOa, Julian J. RIMOLIc *aDepartment of Architecture and Architectural Engineering, Kyoto University Kyoto-Daigaku Katsura, Nishikyo, Kyoto 615-8540, Japan [email protected] b School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA Abstract An optimization method is presented for tensegrity lattices composed of eight truncated octahedral units. The stored strain energy under specified forced vertical displacement is maximized under constraint on the structural material volume. The nonlinear behavior of bars allowing buckling is modeled as a bi- linear elastic material. As a result of optimization, a flexible structure with degrading vertical stiffness is obtained to be applicable to an energy absorption device or a vertical isolation system. Keywords: tensegrity, optimization, strain energy, truncated octahedral unit 1. Introduction Tensegrity structures are a class of self-standing pin jointed structures consisting of thin bars (struts) and cables stiffened by applying prestresses to their members [1, 3]. Because the bars are not continuously connected, i.e., they are topologically isolated from each other, these structures are usually too flexible to be used as load-resisting components of structures in mechanical and civil engineering applications. However, by exploiting their flexibility, tensegrity structures can be utilized as devices for reducing impact forces, isolating dynamic forces, and absorbing energy, to name a few applications [5].
[Show full text]
19. Three-Dimensional Figures
19. Three-Dimensional Figures Exercise 19A 1. Question Write down the number of faces of each of the following figures: A. Cuboid B. Cube C. Triangular prism D. Square pyramid E. Tetrahedron Answer A. 6 Face is also known as sides. A Cuboid has six faces. Book, Matchbox, Brick etc. are examples of Cuboid. B.6 A Cube has six faces and all faces are equal in length. Sugar Cubes, Dice etc. are examples of Cube. C. 5 A Triangular prism has two triangular faces and three rectangular faces. D. 5 A Square pyramid has one square face as a base and four triangular faces as the sides. So, Square pyramid has total five faces. E. 4 A Tetrahedron (Triangular Pyramid) has one triangular face as a base and three triangular faces as the sides. So, Tetrahedron has total four faces. 2. Question Write down the number of edges of each of the following figures: A. Tetrahedron B. Rectangular pyramid C. Cube D. Triangular prism Answer A. 6 A Tetrahedron has six edges. OA, OB, OC, AB, AC, BC are the 6 edges. B. 8 A Rectangular Pyramid has eight edges. AB, BC, CD, DA, OA, OB, DC, OD are the 8 edges. C. 12 A Cube has twelve edges. AB, BC, CD, DA, EF, FG, GH, HE, AE, DH, BF, CG are the edges. D. 9 A Triangular prism has nine edges. AB, BC, CA, DE, EF, FD, AD, BE, CF are the9 edges. 3. Question Write down the number of vertices of each of the following figures: A.
[Show full text]
1 Introduction
Kumamoto J.Math. Vol.23 (2010), 49-61 Minimal Surface Area Related to Kelvin's Conjecture 1 Jin-ichi Itoh and Chie Nara 2 (Received March 2, 2009) Abstract How can a space be divided into cells of equal volume so as to minimize the surface area of the boundary? L. Kelvin conjectured that the partition made by a tiling (packing) of congruent copies of the truncated octahedron with slightly curved faces is the solution ([4]). In 1994, D. Phelan and R. Weaire [6] showed a counterexample to Kelvin's conjecture, whose tiling consists of two kinds of cells with curved faces. In this paper, we study the orthic version of Kelvin's conjecture: the truncated octahedron has the minimum surface area among all polyhedral space-fillers, where a polyhedron is called a space-filler if its congruent copies fill space with no gaps and no overlaps. We study the new conjecture by restricting a family of space- fillers to its subfamily consisting of unfoldings of doubly covered cuboids (rectangular parallelepipeds), we show that the truncated octahedron has the minimum surfacep parea among all polyhedral unfoldings of a doubly covered cuboid with relation 2 : 2 : 1 for its edge lengths. We also give the minimum surface area of polyhedral unfoldings of a doubly covered cube. 1 Introduction. The problem of foams, first raised by L. Kelvin, is easy to state and hard to solve ([4]). How can space be divided into cells of equal volume so as to minimize the surface area of the boundary? Kelvin conjectured that the partition made by a tiling (packing) of congruent copies of the truncated octahedron with slightly curved faces is the solution.
[Show full text]