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Maths Workout - Geometry & Measures Topic 7 - Solids Target 1 Target 2 Target 3 Target 4 Target 5 Identify the number of faces, edges Identify the number of faces, edges Identify the number of faces, edges Identify the number of faces, edges Solve problems and puzzles with and vertices on a range of solids and vertices on a range of solids and vertices on a range of solids and vertices on a range of solids solids Investigate Euler’s formula 1. Observe a range of solids Tasks 1-10. Enter the number of Tasks 1-7. Enter the number of Tasks 1-8. Enter the number of 1. Problem Solving: Recognise the vertices, edges and faces for a... vertices, edges and faces for a... vertices, edges and faces for a... nets of a cube 1. Cube 1. Hexahedron 1. Decagonal prism 2. Observe a range of solids; click to 2. Cuboid 2. Octahedron 2. Dodecagonal prism 2. Engage with the 11 nets of a cube; see a close-up and name observe them fold up 3. Identify the names of solids 3. Triangular prism 3. Octagonal-based pyramid 3. Dodecagonal prism 3. Distinguish between a proper net and a false net 4. Identify the names of solids 4. Triangular-based pyramid 4. Decagonal-based pyramid 4. Cone 4. Distinguish between a proper net and a false net 5. Identify the names of solids 5. Tetrahedron 5. Dodecagonal-based pyramid 5. Cylinder 5. Name a solid from its net 6. Square-based pyramid 6. Hexagonal prism 6. Dodecahedron 6. Problem Solving: Recognise a solid from a limited view 7. Pentagonal-based pyramid 7. Octagonal prism 7. Icosahedron 7. Problem Solving: Recognise a solid from clues 8. Pentagonal-based prism 8. Investigate Euler’s formula 9. Hexagonal-based pyramid 10. Hexagonal-based prism © Smart Interactive Ltd. .

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Geometric Shapes and Cut Sections
GEOMETRIC SHAPES AND CUT SECTIONS MODEL NO: EG.GEO • Wooden and Perspex Material • Long Life and Sturdy • Solid and Hollow sections • Clear Labeling • Small and Large sizes • Magnetic Fractions also Available Object Drawing Models Interpenetration of Solids Models Dissected and Non-Dissected • Two Cylinders of Different Diameters Cube Penetrating Each Other at Right Angles Cone • Two Cylinders of Different Diameters with Sphere Oblique Penetration Cylinder • A Cylinder into a Cone with Oblique Rectangular Prism Penetration Rectangular Pyramid • A Cone & Cylinder with Penetration at Triangular Prism Right Angles Triangular Pyramid • Two Cones at Right Angles Square Prism • Two Square Prisms of Different Sizes at Square Pyramid Right Angles Pentagonal Prism • Two Square Prisms at Oblique Angles Pentagonal Pyramid • Sphere & Cone at Centre Hexagonal Prism • Sphere & Cylinder Eccentric Hexagonal Pyramid • Sphere &Cylinder at Centre Octagonal Prism Octagonal Pyramid Decagonal Prism Decagonal Pyramid Development of Surface for all Shapes *Oblique Polyhedrons for Above Available Available TEACHING AIDS FOR ENGINEERING DRAWING Set of Cut Sectioned Geometric Shapes Set of Solid Wooden Prism and Pyramids Set of Oblique Polyhedrons Set of Geometric Shapes with Development of Surface Paper Nets * Mechmatics reserves the right to modify its Product without notice * In the interest of continued improvements to our products, we reserve the right to change specifications without prior notification. Common Examples of Loci of Point with Pencil tracing position and Theoretical Diagrams * In the interest of continued improvements to our products, we reserve the right to change specifications without prior notification. DEVELOPMENT OF SURFACES MODEL ED.DS A development is the unfold / unrolled flat / plane figure of a 3-D object.
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1 Year 6 – Wednesday 24th June 2020 – Maths Can I identify 3D shapes that have pairs of parallel or perpendicular edges? Parallel – edges that have the same distance continuously between them – parallel edges never meet. Perpendicular – when two edges or faces meet and create a 90o angle. 1 4. 7. 10. 2 5. 8. 11. 3. 6. 9. 12. C1 – Using the shapes above: 1. Name and sort the shapes into: a. Pyramids b. Prisms 2. Draw a table to identify how many faces, edges and vertices each shape has. 3. Write your own geometric definition: a. Prism b. pyramid 4. Which shape is the odd one out? Explain why. C2 – Using the shapes above; 1. Which of the shapes have pairs of parallel edges in: a. All their faces? b. More than one half of the faces? c. One face only? 2. The following shapes have pairs of perpendicular edges. Identify the faces they are in: 2 a. A cube b. A square based pyramid c. A triangular prism d. A cuboid 3. Which shape with straight edges has no perpendicular edges? 4. Which shape has perpendicular edges in the shape but not in any face? C3 – Using the above shapes: 1. How many faces have pairs of parallel edges in: a. A hexagonal pyramid? b. A decagonal (10-sided) based prism? c. A heptagonal based prism? d. Which shape has no face with parallel edges but has parallel edges in the shape? 2. How many faces have perpendicular edges in: a. A pentagonal pyramid b. A hexagonal pyramid c.
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[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.
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WEST SHORE SCHOOL DISTRICT Math Learning Module 5 Title of Module Module 5: Addition and Multiplication with Grade Level 5th Grade Volume and Area Curriculum Area Math Time Frame enVision Math Topic 10, Topic 15 (MP 3) Best Practices MP# 1. Make sense of problems and persevere in solving them MP# 2. Reason abstractly and quantitatively MP# 4. Model with mathematics MP# 3. Construct viable arguments and critique the reasoning of others MP# 5. Use appropriate tools strategically MP# 6. Attend to precision MP# 7. Look for and make use of structure (Deductive Reasoning) MP# 8. Look for and express regularity in repeated reasoning Transfer Goals 1. Interpret and persevere in solving complex mathematical problems using strategic thinking and expressing answers with a degree of precision appropriate for the problem context. 2. Express appropriate mathematical reasoning by constructing viable arguments, critiquing the reasoning of others, and attending to precision when making mathematical statements. 3. Apply mathematical knowledge to analyze and model mathematical relationships in the context of a situation in order to make decisions, draw conclusions, and solve problems. Key Learnings/Big Ideas Through the daily use of area models, the fraction module prepares students for an in-depth discussion of area and volume in Module 5. But the module on area and volume also reinforces work done in the fraction module: Now, questions about how the area changes when a rectangle is scaled by a whole or fractional scale factor may be asked. Measuring volume once again highlights the unit theme, as a unit cube is chosen to represent a volume unit and used to measure the volume of simple shapes composed out of rectangular prisms.
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3D Geometry: Chapter Questions 1. What Are the Similarities And
3D Geometry: Chapter Questions 1. What are the similarities and differences between prisms and pyramids? 2. How are polyhedrons named? 3. How do you find the cross-section of 3-Dimensional figures? 4. How do you find the volume of a prism or cylinder? 5. How are the volumes of prisms and pyramids related? 6. How do you find the Surface Area of a 3-Dimensional Figure? 3D Geometry: Chapter Problems 3 Dimensional Solids Class Work In 1-5, name the figure. 1. 2. 3. 4. 5. In 6-10, give the number faces, edges, and vertices of each shape. 6. 7. 8. 9. triangular pyramid 10. square prism Homework In 11-15, name the figure. 11. 12. 13. 14. 15. In 16-20, give the number faces, edges, and vertices of each shape. 16. 17. 18. 19. octagonal pyramid 20. rectangular prism Nets Class Work In 21-25, identify the 3-dimensional figure from its net. 21. 22. 23. 24. In 25-28, draw the net for the stated figure. 25. Rectangular Pyramid 26. A soda can 27. A die 28. A piece of pizza Homework In 29-32, identify the 3-dimensional figure from its net. 29. 30. 31. 32. In 33-36, draw the net for the stated figure. 33. Hexagonal Prism 34. A car tire 35. A 4x4 fence post 36. A piece of apple pie Volume of Prisms and Cylinders Class Work Find the volume of each figure. 37. 38. 39. 40. A 5 m x 3 m x 4 m rectangular prism 41. A cube with edge of 6 ft 42.
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Arxiv:2006.11342V1 [Math.MG] 19 Jun 2020 a TV Game Map, Rather Than the Four Required on the Plane
A Simple 3D Isometric Embedding of the Flat Square Torus J. Richard Gott III∗ 1 and Robert J. Vanderbei 2 1Department of Astrophysical Sciences 2Department of Operations Research and Financial Engineering Princeton University, Princeton, NJ, 08544, USA Abstract Start with Gott (2019)'s envelope polyhedron (Squares|4 around a point): a unit cube missing its top and bottom faces. Stretch by a factor of 2 in the vertical direction so its sides become (2 × 1 unit) rectangles. This has 8 faces (4 exterior, 4 interior), 8 vertices, and 16 edges. F −E +V = 0, implying a (toroidal) genus = 1. It is isometric to a flat square torus. Like any polyhedron it has zero intrinsic Gaussian curvature on its faces and edges. Since 4 right angled rectangles meet at each vertex, there is no angle deficit and zero Gaussian curvature there as well. All meridian and latitudinal circumferences are equal (4 units long). 1 Introduction Many video games including Pac-Man and Asteroids are played on a square TV screen with a toroidal geometry. Pac-Man, or a spaceship that disappears off the top of the screen immediately reappears at the bottom at same horizontal location. Likewise, if Pac-Man or a spaceship disappears off the right-hand edge of the screen it immediately reappears on the left-hand edge of the screen at the same vertical location. These games thus have a square Euclidean flat geometry but a toroidal topology. It takes seven colors in general to color nations on such arXiv:2006.11342v1 [math.MG] 19 Jun 2020 a TV game map, rather than the four required on the plane.
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Convex Segmentochora
Convex Segmentochora Dr. Richard Klitzing [email protected] updated version (June 2015) of preprint (August 2001), published in: Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 Abstract Polytopes with all vertices both (A) on a (hyper-) sphere and (B) on a pair of parallel (hyper-) planes, and further (C) with all edges of equal length I will call segmentotopes. Moreover, in dimensions 2, 3 and 4 names like segmentogon, segmentohedron, and segmentochoron could be used. In this article the convex segmentotopes up to dimension 4 are listed. 1 Introduction About 150 years of highdimensional research on polytopes have passed. The regular ones are well-known since those days: in 1852 L. Schlaefli completed his monograph on polyschemes. About 20 years after N. Johnson in 1966 had published the set of convex polyhedra with regular faces, Mrs. R. Blind had done the corresponding research in higher dimensions for polytopes with regular facets. The convex uniform ones of dimension 4 are readily listed on the website http://member.aol.com/_ht_b/Polycell/uniform.html1, and the complete list of all uniform ones of dimension 4 is still ongoing (J. Bowers and G. Olshevsky). Sure, polychora, i.e. polytopes of dimension 4, are not so easy to visualize. This is especially due to the fact that for this attempt the 4th dimension has to be projected somehow into the span of the other 3 directions. One possibility, to do this, works rather well for figures with just one edge length. It shows the 4th dimension as a contraction.
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Convex Polyhedra with Regular Faces
CONVEX POLYHEDRA WITH REGULAR FACES NORMAN W. JOHNSON 1. Introduction. An interesting set of geometric figures is composed of the convex polyhedra in Euclidean 3-space whose faces are regular polygons (not necessarily all of the same kind). A polyhedron with regular faces is uniform if it has symmetry operations taking a given vertex into each of the other vertices in turn (5, p. 402). If in addition all the faces are alike, the polyhedron is regular. That there are just five convex regular polyhedra—the so-called Platonic solids—was proved by Euclid in the thirteenth book of the Elements (10, pp. 467-509). Archimedes is supposed to have described thirteen other uniform, "semi-regular" polyhedra, but his work on the subject has been lost. Kepler (12, pp. 114-127) showed that the convex uniform polyhedra consist of the Platonic and Archimedean solids together with two infinite families—the regular prisms and antiprisms. It was Kepler also who gave the Archimedean polyhedra their generally accepted names. It is fairly easy to show that there are only a finite number of non-uniform regular-faced polyhedra (11; 13), but it is no simple matter to establish the exact number. However, it appears that there are just ninety-two such solids. Some special cases were discussed by Freudenthal and van der Waerden (8), and a more general treatment was attempted by Zalgaller (13). Subsequently, Zalgaller et al. (14) determined all the regular-faced polyhedra having one or more trivalent vertices and all those having only pentavalent vertices. Griin- baum and Johnson (9) proved that the only kinds of faces that a regular-faced solid, other than a prism or an antiprism, may have are triangles, squares, pentagons, hexagons, octagons, and decagons.
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CUBE BUILDINGS Activity 2 Hy Kim, Jan Marie Popovich and Alice Hruska Fold a New Square to Obtain These Four Triangles and Two Parallelograms
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A Simple 3D Isometric Embedding of the Flat Square Torus
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