Understanding symmetry elements and operations, twinning in minerals, and miller indices of planes is important in mineralogy and crystallography. This video covers the 4 major symmetry operations (mirrors, rotation axes, centers of symmetry or inversion, and rotoinversion axes), twinning (twin elements such as twin planes, twin axes, and twin centers, and types of twinning such as contact twins, penetrated twins, and multiple twins), and miller indices of cleavage planes (first I go over what a mineral lattice and unit cell is then a miller index, how to figure out a miller index, then we do practice!), lastly we go over the importance of miller indices (determining d-spacing with miller indices and x-ray diffraction (XRD), as well as Bragg's Law!). This lecture leads into the upcoming lectures on XRD and optical mineralogy. Reference: Chapter 5 in Earth Materials by Cornelis Klein GEO GIRL Website: (visit my website to see all my courses, shop merch, learn more about me, and donate to support the channel if you'd like!) 0:00 4 symmetry operations 0:38 mirrors and rotation axes 5:06 centers of symmetry or inversion 6:17 rotoinversion axes 7:01 twinning crystals 10:14 cleavage planes & miller indices 11:41 unit cells in crystal lattices 14:06 miller indices explained 18:15 miller indices practice 27:54 why do miller indices matter? 30:37 upcoming content! 32:31 bloopers Hey there, Earth enthusiast! Check my favorite Earth-friendly products: Bamboo toilet paper: Bamboo paper towels: Compostable tableware: Compostable trash bags: Bamboo cutlery + straw! : Eco-Friendly Tote (great for grocery shopping!): Reusable straws + cleaning brushes (my fav!): Eco-friendly laundry detergent: Directly offset your carbon footprint with Wren: (Just click link, press get started, take the free C footprint quiz, then choose how much you want to reduce your footprint by donating to the C sequestration projects they're funding!) Non-textbook books I recommend: Oxygen by D. Canfield: Brief history of Earth by A. Knoll: Life on young planet by A. Knoll: Some assembly required by N. Shubin: Your inner fish by N. Shubin: Oxygen by N. Lane: Alien Oceans by K. Hand: Life's Engines: Tools I use as a geologist/teacher/student: Geology field notebook: Geology rock hammer: Geological compass: Geological hand lens: Camera: Carbon-neutral pencil bag: Carbon-neutral backpack: Image sources: : Other figures from book: Disclaimer: Links included in this description might be affiliate links. If you purchase a product or service with the links that I provide I may receive a small commission, but there is no additional charge to you! Thank you for supporting my channel so I can continue to provide you with free content each week! And as always, let me know your topic suggestions in the comments down below!