From the course: Deke's Techniques (2018-2021)
738 Introducing the Pentagon Patterns
From the course: Deke's Techniques (2018-2021)
738 Introducing the Pentagon Patterns
- Hey gang, this is Deke McClelland, welcome to Deke's Techniques. Now this week marks the beginning of a deep dive that we're about to take, on a topic that I hope will interest those of you who are passionate about repeating tile patterns, i.e. tessellations. So, while it probably escaped your notice, this year marks the 100th anniversary of the discovery of, get this, the first tessellating irregular convex pentagon. And I know you're probably thinking, my word that is the best news I've ever heard, except for the part where I don't have the remotest idea of what you're talking about. So let me explain, if you will. We'll start with the three sided shape, aka triangle. Any triangle you draw with tessellate. So click three times with the pen tool, rotate the shape 180 degrees, and away you go. Then we have four sided shapes which are known as quadralaterals, they also tessellate. So this guy right here is an irregular one, but I've rotated it to four different angles and it tessellates beautifully, and this goes for parallelograms, as well as rectangles and, of course, squares. Then we have six sided shapes, i.e. hexagons. There are three types of hexagons that tessellate including this guy right here, which is type three by the way. They all include regular hexagons, which you already know tessellate because Illustrator and other programs offer hex patterns. What about shapes with seven, eight, or nine sides? Well if they're convex, and I'll show you what I mean by that in a moment, they cannot possibly tessellate, which leaves us with a missing shape, the five sided shape, or pentagon. Now the ancient Greeks proved that regular pentagons, like the Pentagon building in Washington, D.C. can not tessellate, but they suspected that there might be an irregular convex pentagon that could. They never found it, neither did the great pattern makers of Arabia. It wasn't until 1918 when a German mathematician named Karl Reinhardt discovered five types of tessellating pentagons, and when I say types I don't mean specific shapes, I mean classes of shapes. So for example, this is an example right here of type four but so this is, and they look very different than each other. Now over the years, more of these pentagons have been discovered and these days we know about 15 of them including this guy right here, type 15, which was discovered in the year 2015, get that. And notice, if you will, that it's the same pentagon rotated to 12 different angles. Now this might seem pretty complicated but I'm gonna make it absolute child's play starting inside this very movie. All right, let's start things off with a quick overview of the basic styles of five sided shapes, that is to say pentagons, that we have to work with. Starting with the regular pentagon which is the kind of pentagon you can create using the polygon tool here inside Illustrator. Now notice, where the diagram is concerned, that the angles between the sides appear in bold and then length of the sides appear in italics. And so for any regular polygon, each and every one of the angles equals 108 degrees, and if you take 108 and multiply it times five then you end up with 540 degrees which is the total angle value for any five sided shape. Meanwhile, where a regular pentagon is concerned, the length of each and every side is identical. Now something else I want you to note, as least when working in Illustrator, is that the program measures pentagons and other regular polygons, and so notice if I select the shape, that I've gone ahead and identified the center, and so if I were to grab the line segment tool and then I need to make sure that my smart guides are turned on so I can see the heads up display, I'll go ahead and drag from that center to any one of the anchor points along the perimeter of the shape, and you can see that my distance value right there is 170 points, which tells me the length of that line. And so it doesn't matter which one of these anchor points I drag to, I'm gonna get that same value. And so I'll just go ahead and get rid of that line and then I'll select the polygon tool, from the shape tool fly out menu, and I'll go ahead and click on that center point in order to bring up the polygon dialogue box, I'll change the number of sides to five, and then I'll shift tab to the radius value, and I'll take it up to 170 points just as I saw a moment ago, and I'll click okay, and I end up with that exact same shape. And here inside the Illustrator CC, I can click on the word shape up here in the horizontal control panel, at which point I can change the number of sides if I want to, and I can change that radius value, and Illustrator does a good job of showing you what the radius looks like, at least where a hexagon is concerned. In any event, the problem where a regular pentagon is concerned, is that it doesn't tessellate properly. And so notice, if I turn on this layer right here, and I'll go ahead and deselect the artwork as well, that I've done my best to create a repeating pattern using that regular pentagon, but it just so happens it's impossible to tile a regular pentagon monohedrally, this is to say with a single tile, at least at 2D Euclidean space, in other spaces you can do some wacky stuff, but where two dimensional design is concerned, 108 degrees doesn't divide evenly into a 360 degree circle and so we end up with these diamond shaped gaps in between. All right, I'll go ahead and turn off that layer and I will switch to the next artboard so that we can see a second style of pentagon which is an irregular non-convex shape. And so what we have here is a group of five different angles, identified in bold once again, which add up to 540 degrees, however, they can all be different, and you can have one indent, which I've identified here in red, or it is possible to have a pentagon with two indents but I've never seen one tessellate. Meanwhile, your sides can be any length whatsoever. And so if we were to take this shape, the one we're currently seeing, and repeat it by rotating, flipping, and moving it around, then you can see that it tessellates wonderfully. The problem is, no one's really classified how many varieties of these irregular non-convex repeating pentagons that there are. And so while it's very cool, this is not something that we're gonna delve into in this particular technique. Instead, we're gonna take a look at irregular convex pentagons which look like this guy right here. And so notice that once again, all of our angles add up to 540 degrees, we have no indents, hence the word convex up here, and once again our sides can be any length. And so over the last 100 years, and to this very date, 15 types of irregular convex pentagons are known to tile monohedrally including the one that we're seeing here, which is known as a type five pentagon, and the reason they're called types is because they're not specific shapes, in other words, a type five pentagon doesn't have to look exactly like this guy here, rather the varieties of shapes as we'll see. And that's my overview of the basic varieties of pentagons that you can't and sometimes can tessellate monohedrally, that is by taking a single shape and rotating, flipping, and/or moving it, not only here inside Illustrator, but in 2D space. All right, so are you excited? I hope so, because next week we're gonna begin our look at every single one of those 15 types starting with the first five types from Karl Reinhardt. Deke's Techniques each and every week, you've gotta keep watching.
Practice while you learn with exercise files
Download the files the instructor uses to teach the course. Follow along and learn by watching, listening and practicing.
- 669_custom_QR.zip
- 670_more_QR.zip
- 671_hidden_circles.zip
- 673_shade_panels.zip
- 672_more_rectangles.zip
- 674_cafe_wall.zip
- 675_skewed_walls.zip
- 676_magic_checkers.zip
- 677_magic_dots.zip
- 678_reverse_illusion.zip
- 679_illusion_decor.zip
- 680_more_gizmos.zip
- 681_connect_gizmos.zip
- 682_wifi_symbol.zip
- 683_bluetooth_logo.zip
- 684_trajan_color.zip
- 685_trajan_AIcc.zip
- 686_stylistic_PsCC.zip
- 687_stylistic_AIcc.zip
- 688_grad_molecules.zip
- 689_sharper_moles.zip
- 690_smart_cules.zip
- 691_explore_cules.zip
- 692_blend_cules.zip
- 693_high_pass_cules.zip
- 694_cell_pattern.zip
- 695_hemoglobin.zip
- 696_edgy_cells.zip
- 697_springy_cells.zip
- 698_accordian_letters.zip
- 699_skew_blends.zip
- 700_cross_blends.zip
- 701_slice_blend.zip
- 702_blend_distort.zip
- 703_dynamic_roughen.zip
- 704_fish_twist.zip
- 705_dynam_bgnd_1.zip
- 706_dynam_bgnd_2.zip
- 707_quieter_art.zip
- 708_disintegration.zip
- 709_more_flakes.zip
- 710_mask_ashes.zip
- 711_flakes_to_ash.zip
- 712_note_tool.zip
- 713_contour_map.zip
- 714_contour_grad.zip
- 715_contour_arb.zip
- 716_contour_riff.zip
- 717_smooth_contour.zip
- 718_contour_cash.zip
- 719_color_of_money.zip
- 720_AI_adjust.zip
- 721_computer_key.zip
- 722_key_type.zip
- 723_faux_hedcut.zip
- 724_hedcut_lines.zip
- 725_color_hedcut.zip
- 726_ET_moon.zip
- 727_ET_trees.zip
- 728_ET_TRex.zip
- 729_global_glow.zip
- 730_content_aware.zip
- 731_space_portal.zip
- 732_enhance_portal.zip
- 733_rushing_stars.zip
- 734_AIcc_puppet.zip
- 735_puppet_tricks.zip
- 736_complex_puppet.zip
- 737_puppet_shortcut.zip
- 738_pentagons.zip
- 739_reinhardt.zip
- 740_kershner.zip
- 741_james_pentagon.zip
- 742_rice_pentagons.zip
- 743_stein_pentagon.zip
- 744_15th_pentagon.zip
- 745_tessellate_15.zip
- 746_pentatiles.zip
- 747_mod_pattern.zip
- 748_complement_tiles.zip
- 749_image_pattern.zip
- 750_pattern_fit.zip
- 751_candy_keeper.zip
- 752_keeper_text.zip
- 753_monster_movie.zip
- 754_mono_halftone.zip
- 755_word_haunted.zip
- 756_cheat_letters.zip
- 757_alt_adjust.zip
- 758_scuba_mono.zip
- 759_backscatter.zip
- 760_sample_outside.zip
- 761_Ps_vector_logo.zip
- 762_trans_shapes.zip
- 763_photo_logo.zip
- 764_high_res_snow.zip
- 765_enhance_snow.zip
- 766_snowflake_bokeh.zip
- 767_mandala_ps.zip
- 768_mandala_pattern.zip
- 769_mandala_dots.zip
- 770_mandala_color.zip
- 771_mandala_final.zip
- 772_AI_trim_view.zip
- 773_AI_presentation.zip
- 774_global_edits.zip
- 775_global_control.zip
- 776_freeform_grads.zip
- 777_freeform_lines.zip
- 778_freeform_gotcha.zip
- 779_great_white.zip
- 780_sharper_shark.zip
- 781_vibrance_sat.zip
- 782_vib_sat_sharp.zip
- 783_hedcut_action.zip
- 784_action_actions.zip
- 785_color_lines.zip
- 786_combine_lines.zip
- 787_clip_to_group.zip
- 788_color_outside.zip
- 789_flip_horizontal.zip
- 790_white_walker.zip
- 791_walker_begins.zip
- 792_digital_shave.zip
- 793_deep_wrinkles.zip
- 794_deep_brows.zip
- 795_pale_lips.zip
- 796_glowing_blue.zip
- 797_lifeless_pupils.zip
- 798_cold_gloomy.zip
- 799_brittle_flakes.zip
- 800_trans_shapes.zip
- 801_range_mask.zip
- 802_flip_photo.zip
- 803_actual_dream.zip
- 804_augment_dream.zip
- 805_smart_distortions.zip
- 806_blend_distortions.zip
- 807_star_negative.zip
- 808_star_pattern.zip
- 809_shaded_stars.zip
- 810_grad_pattern.zip
- 811_pattern_fade.zip
- 813_gobstopper.zip
- 814_gobpattern.zip
- 815_galignment.zip
- 816_etched_lines.zip
- 817_blend_pattern.zip
- 818_cubical_holes.zip
- 819_grad_pattern.zip
- 820_iso_arrows.zip
- 821_position_tips.zip
- 822_fill_gaps.zip
- 823_cartoon_teeth.zip
- 824_triangle_eye.zip
- 825_add_windows.zip
- 826_perfect_tessellate.zip
- 827_triangle_tunnels.zip
- 828_triangles_pattern.zip
- 829_colorful_triangles.zip
- 830_recolor_triangles.zip
- 831_rainbow_blends.zip
- 832_pattern_blends.zip
- 833_imposs_trident.zip
- 834_shade_trident.zip
- 835_opposing_grads.zip
- 836_trident_shadows.zip
- 837_impossible_hex.zip
- 838_impossible_lattice.zip
- 839_Joan_Miro.zip
- 840_watercolor_wash.zip
- 841_Miro_signature.zip
- 842_Photoshop_Miro.zip
- 843_enlarge_Miro.zip
- 844_Miro_Peele.zip
- 845_color_Us.zip
- 846_red_rorschach.zip
- 847_finish_Us.zip
- 848_CAF_fails.zip
- 849_turkey_2019.zip
- 850_trace_hand.zip
- 851_articulated_hand.zip
- 852_colorful_hand.zip
- 853_paint_fingernails.zip
- 854_paint_turkey.zip
- 855_turkey_feathers.zip
- 856_drop_shadow.zip
- 857_Ps_iPad_1.zip
- 858_Ps_iPad_2.zip
- 859_Ps_iPad_3.zip
- 860_iPad_Sidecar.zip
- 861_Adobe_Fresco.zip
- 862_Fresco_halftones.zip
- 863_live_brushes.zip
- 864_oil_paint.zip
- 865_Fresco_masks.zip
- 866_repurpose_mask.zip
- 867_vector_brush.zip
- 868_fresco_ps.zip
- 869_auto_color.zip
- 870_ACR_pano.zip
- 871_correct_pano.zip
- 872_diffusion.zip
- 873_simplify_2020.zip
- 874_fill_gaps.zip
- 875_posterize.zip
- 876_paint_bucket.zip
- 877_nonD_poster.zip
- 878_dynamic_poster.zip
- 879_filmstrip.zip
- 880_awful_awesome.zip
- 881_rembrandt.zip
- 882_recolor_freeform.zip
- 883_recolor_group.zip
- 884_over_under.zip
- 885_dev_over_under.zip
- 886_3D_metal_star.zip
- 887_heavy_metal.zip
- 888_wonder_poster.zip
- 889_wonder_displace.zip
- 890_wonder_woman.zip
- 891_metadata_template.zip
- 892_edit_metadata.zip
- 893_quilt_warp.zip
- 894_warp_object.zip
- 895_gopro_images.zip
- 896_content_aware.zip
- 897_gopro_combo.zip
- 898_blend_vignette.zip
- 899_photo_painting.zip
- 900_cue_ball.zip
- 901_pool_ball.zip
- 902_stripe_ball.zip
- 903_transform_each.zip
- 904_recolor_pool.zip
- 905_pool_cues.zip
- 906_rotate_cues.zip
- 907_repeat_face.zip
- 908_rainbow_faces.zip
- 909_mask_lips.zip
- 910_single_many.zip
- 911_symmetrical_mask.zip
- 912_colorize_grads.zip
- 913_mask_grads.zip
- 914_lantern_type1.zip
- 915_lantern_type2.zip
- 916_lantern_type3.zip
- 917_blend_steps.zip
- 918_blended_blends.zip
- 919_reverse_order.zip
- 920_pattern_colors.zip
- 921_blend_pattern.zip
- 922_polygons.zip
- 923_equil_triangle.zip
- 924_mercedes.zip
- 925_star_ring.zip
- 926_perfect_star.zip
- 927_lets_review.zip
- 928_basic_shapes.zip
- 929_triangle_man.zip
- 930_paint_grads.zip
- 931_adv_grads.zip
- 932_trans_vectors.zip
- 933_free_distort.zip
- 934_dynamic_fx.zip
- 935_cats_eye.zip
- 936_cat_iris.zip
- 937_primitives.zip
- 938_zig_zag.zip
- 939_dynamic_hilight.zip
- 940_reptile_scales.zip
- 941_shade_eye.zip
- 942_variable_shade.zip
- 943_dragon_eye.zip
- 945_single_thumbnail.zip
- 946_ai_home.zip
- 947_unlock_object.zip
- 948_unlock_icon.zip
- 949_line_tool.zip
- 950_broken_candy.zip
- 951_candy_rhino.zip
- 952_wrap_pattern.zip
- 953_ice_shadows.zip
- 954_illustrator_ipad.zip
- 955_pencil_points.zip
- 956_ipad_blob.zip
- 957_ipad_pen.zip
- 958_grads_repeats.zip
- 959_color_grading.zip
- 960_grading_tricks.zip
- 961_blend_balance.zip
- 962_font_height.zip
- 963_camera_profile.zip
- 964_JPEG_raw.zip
- 965_match_detail.zip
- 966_Ps_line_tool.zip
- 967_troubleshoot_line.zip
- 968_blend_vectors.zip
- 969_curve_line.zip
- 970_point_glyphs.zip
- 971_area_glyphs.zip
- 972_snap_glyphs.zip
- 973_snap_letterform.zip
- 974_glyph_shape.zip
- 975_glyph_pen.zip
- 976_playing_cards.zip
- 977_scale_shape.zip
- 978_card_suits.zip
- 979_enhance_path.zip
- 980_power_symbol.zip
- 981_huge_artboard.zip
- 982_new_artboard.zip
- 983_triceratops.zip
- 984_pen_tricks.zip
- 985_round_corner.zip
- 986_draw_round.zip
- 987_reshape_round.zip
- 988_AI_brushed.zip
- 989_AI_rivets.zip
- 990_blend_grad.zip
- 991_binoculars.zip
- 992_blue_halo.zip
- 993_bi_aberrations.zip
- 994_hide_shapes.zip
- 995_subwoofer.zip
- 996_deep_cone.zip
- 997_gradient_frame.zip
- 998_hex_screws.zip
- 999_thats_all.zip
Contents
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669 Customizing a QR code in Photoshop11m 22s
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670 Adding more color to your QR code4m 29s
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671 Coffer illusion and the hidden circles18m 10s
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672 Filling out the hidden circles illusion9m 30s
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673 Shading the panels in a Coffer illusion13m 1s
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674 Drawing a classic “café wall” illusion11m 20s
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675 Skewing your crazy café walls in Illustrator9m 25s
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676 Creating a “magical checkers” illusion20m 8s
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677 Swapping magical checkers for dots8m 35s
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678 Reversing the direction of your illusion8m 33s
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679 Decorating your illusion9m 47s
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680 Adding more and more gizmos11m 52s
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681 Connecting the gizmos wirelessly4m 59s
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682 Drawing a Wi-Fi symbol in Illustrator9m 48s
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683 Drawing the official Bluetooth logo10m 8s
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684 Introducing Trajan Color Concept13m 10s
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685 Trajan Color Concept in Illustrator CC7m 10s
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686 Using stylistic sets in Photoshop CC9m 37s
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687 Using stylistic sets in Illustrator CC6m 47s
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688 Creating gradient molecules in Photoshop10m 17s
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689 Sharpening your very soft molecules4m 41s
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690 Editing your smart-filtered molecules6m 32s
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691 Exploring regular molecule patterns17m 41s
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692 Blending opposing rows of colorful molecules8m 49s
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693 Sharpening molecules with High Pass6m 3s
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694 Creating shimmering cells in Illustrator12m 25s
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695 Turning regular hexagons into organic cells11m 50s
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696 Enhancing your organic cells in Photoshop8m 58s
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697 Making dead cells spring to life7m 41s
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698 Creating letters with accordion extrusions13m 58s
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699 Combining object blends with skews11m 28s
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700 Making one object blend cut through another9m 44s
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701 Making one object blend slice across another13m 27s
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702 Object blends and dynamic distortions in Illustrator8m 11s
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703 Another random distortion: Roughen7m 57s
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704 Dynamic warp distortions: Fish and Twist8m 52s
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705 Adding a dynamic background, part 110m 14s
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706 Adding a dynamic background, part 27m 44s
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707 “Quieting down” an overly elaborate design9m 25s
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708 The Marvel disintegration effect9m 14s
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709 Building up more flakes and ashes7m 33s
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710 Enhancing and masking your disintegration8m 12s
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711 Turning your flakes into dull, dead ash4m 10s
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712 Jogging your memory with the Note tool9m 59s
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713 Contour mapping with Distort > Displace10m 23s
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714 Contour map + gradient map6m 54s
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715 Contour map + arbitrary map8m 22s
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716 Riffing on a contour map in Photoshop5m 24s
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717 Smoothing out jagged contour lines4m 11s
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718 Contour mapping for cash in Photoshop9m 27s
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719 Infusing an image with the color of money2m 53s
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720 Simulating an adjustment layer in Illustrator9m 25s
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721 Drawing a stylish computer key12m 9s
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722 Spelling a word in computer keys6m 55s
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723 Creating a faux hedcut in Photoshop13m 7s
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724 Tracing outlines around your hedcut7m 47s
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725 Creating a full-color hedcut effect7m 32s
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726 Creating an E.T. moon in Photoshop8m 42s
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727 Adding a forest of trees for your E.T. moon10m 41s
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728 Combining the best of E.T. and Jurassic Park10m 59s
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729 Tracing vectors with a universal glow6m 17s
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730 Creative uses for Content-Aware Fill11m 47s
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731 Creating a porthole to a far-away galaxy7m 42s
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732 Enhancing your crazy space porthole7m 3s
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733 Creating a galaxy of rushing stars5m 42s
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734 Using the Puppet Warp tool in Illustrator CC6m 7s
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735 Illustrator Puppet Warp tips and tricks7m 20s
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736 Puppet-Warping very complicated selections6m 18s
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737 Shift-P for Puppet Warp!2m 59s
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738 Introducing the Pentagon Patterns7m 29s
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739 Types 1–5: The Reinhardt pentagons14m 17s
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740 Types 6–8: The Kershner pentagons5m 47s
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741 Type 10: The James pentagon5m 53s
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742 Types 9, 11, 12, and 13: The Rice pentagons7m 58s
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743 Type 14: The Stein pentagon3m 53s
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744 Creating a type 15 pentagon in Illustrator9m 27s
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745 Tessellating your type 15 pentagon14m 22s
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746 Expressing pentagons as proper tile patterns12m 9s
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747 Applying and modifying a tile pattern11m
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748 Combining complementary patterns7m 43s
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749 Combining a tile pattern with a photograph6m 33s
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750 Adjusting a tile pattern to fit its photo5m 36s
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751 Creating a creepy Candy Keeper in Photoshop3m 59s
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752 Enhancing the Candy Keeper text4m 46s
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753 Creating an old monster movie poster7m 3s
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754 Adding a monochrome halftone effect4m 3s
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755 Enhancing a special word, such as “Haunted”4m 27s
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756 Cheating letters into an ancient border2m 25s
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757 Naming an adjustment layer as you create it4m 13s
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758 Under the sea in strict monochrome6m 29s
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759 Backscatter and split toning7m 21s
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760 Sampling any color outside Photoshop3m 17s
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761 Designing a vector-based logo in Photoshop9m 20s
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762 Free-transforming shape layers7m 56s
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763 Adding a photo element to your vector logo6m 34s
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764 High-resolution snowflakes in Photoshop5m 45s
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765 Enhancing your big, juicy snowflakes7m 19s
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766 Adding a snowflake bokeh “on the lens”6m 8s
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