From the course: Deke's Techniques (2018-2021)
743 Type 14: The Stein pentagon
From the course: Deke's Techniques (2018-2021)
743 Type 14: The Stein pentagon
- [Instructor] In this movie we'll take a look at type 14 of the perfectly tessellating irregular convex pentagons. And to see what that looks like, I'm gonna bring up the art boards panel by going up to the window menu and choosing the art boards command. And that way I can easily switch between a couple of art boards down here near the bottom of the list. So I'm gonna double click on type 14 in order to advance to this guy right here, which was discovered by a German math student named Rolf Stein back in 1985. And as I hope you'll remember by now, all the angles appear in bold right here, all five of them, and the sides appear in italics. And so notice we have some pretty familiar rules. A equals 90 degrees so we've got a right angle at this location. Two B plus C equals 360 degrees whereas C plus E equals 180 degrees. And if that does by any chance look familiar, it's because those are the same angle rules that we saw with type 11, which was created by Marjorie Rice. So the very same angle rules prevail. Though, as we'll see, they're more specific this time around. Notice that the sides where type 11 are concerned, d equals e equals two-a plus c. Compare that to type 14, where d and e still are equal to each other. But so are a and c this time around. So the length of side a is the same as the length of side c, and if you multiply either of them times two, you get d or e. We also have some very specific angle instructions that go beyond what I've listed here. And to see what that looks like, even though it's a little bit scary, I'm gonna return to the layers panel and I'm gonna turn on this layer right here, this demos layer. And notice that just for B, this is just one of the rules associated with angle B, the sign of B is equal to the square root of 57 minus three, all over eight, which happens to equal this value right here. So 0.568 and so forth. And then if you do an arc sign to figure out what B is equal to, it's 145.3383362 degrees and so forth. So rather than sharing all this information with you, which probably isn't gonna do you that much good, I've gone ahead and approximated each one of these angles, which is why they appear in beige. So I'll go ahead and turn off that layer. B is approximately 145.34 degrees, C is 69.32, D is 124.66, and you can probably read just as well as I can, that E is approximately equal to 110.68 degrees. And to see what that looks like, I'll go ahead and turn on the patterns layer here. And this time we still have these kind of fish faces, but we have these tails as well. And so to put those together, and again, you can approach your patterns in any way you like and still get the exact same effects. I went ahead and started with this first shape and I flipped it across the horizontal axis. So we've got a vertical flip. And then I took that second shape and I duplicated it, and then I rotated it 55.28 degrees in order to create this kind of fish tail or body or what-have-you. And then I took all three of these shapes and rotated them 180 degrees. So we end up with this kind of Pisces orientation. And so I'm gonna go ahead and turn those two layers off for a moment. I want you to see the ultimate difference between type 14 and type 11. So I'll go ahead and switch back to the art boards panel, which may be located at a different location on your screen, and I'll double click on type 11. So here you can see that I've duplicated that base tile a total of eight times in order to achieve this final pattern, whereas with type 14, we're repeating that tile just six times. And that is type 14 of the perfectly tessellating irregular convex pentagons first discovered by German math student Rolf Stein back in 1985.
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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