Perfect Shapes in Higher Dimensions - Numberphile

  • Published on Mar 23, 2016
  • Carlo Sequin talks through platonic solids and regular polytopes in higher dimensions.
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Comments • 5 640

  • GekkoTadpole 247

    Waiting for when we can get Dungeons and Dragons-style dice sets modeled after each of those wireframes-

  • parween heiser
    parween heiser 2 days ago

    What happens at 10 dimensions?

  • Entity #002 {Formerly Mr. Anomalous}

    Came to learn about hyperdimensional geometry, stayed for the Swiss accent.

  • 247 Stoned
    247 Stoned 2 days ago


  • Nicole
    Nicole 2 days ago

    I clicked because the thumbnail reminds me of the monstrous geometric angels in Evangelion lol. [screams geometrically]

  • Screw The Net
    Screw The Net 3 days ago +1

    You didnt say how many symmetries the 120 cell had!! WHYYY!! T>T I say it has 28800 symmetries. Thought? o>O

  • Inoxia1234
    Inoxia1234 3 days ago

    24:00 hellraiser is real...

  • cursed alien
    cursed alien 3 days ago

    The 3D Platonic solids are all the dnd dice except for the d10

  • intergalactic snail
    intergalactic snail 3 days ago

    Is this the thing from neon Genesis evangelion?

  • André Paulsen
    André Paulsen 3 days ago

    7:05 Go Utah!

  • Maxsurlek
    Maxsurlek 4 days ago

    24:30 A perfectly square monitor. What else would he use?

  • M.H.0903
    M.H.0903 4 days ago +1

    Can someone answer this question for me?
    Do objects that exist within the presumed 11 dimensions have to exist in all 11? Like, does the human body extent into higher dimensions without us realising OR can objects exist up to 3D/6D/7D etc.
    Also, are the shapes he is holding in the video bending into 4D space or are they trapped in 3D?

  • Pocom
    Pocom 5 days ago

    1:35 these are dices for D&D

  • Eyeswideopen 333
    Eyeswideopen 333 5 days ago

    3d boring. We were 5th dimensional beings, but due to the powers that be, through indoctrination, foods, liquids, frequencies most are stuck in the 3rd. Alignment of the chakras, raising our kundalini to awaken the 3rd 👁 puts you in the 5th and you will see the truth of everything that is really here. The earth is rising so most people’s vibration will get higher. There’s 11 dimensions, but most wont get anywhere near it. Don’t put restrictions on yourself.

  • 色々大好きおじさん


  • Nathaniel Rosegg
    Nathaniel Rosegg 7 days ago

    If you want to visualise the 4th dimension, inhale vaporized N,N DMT crystals

  • Jeffrey Saker
    Jeffrey Saker 7 days ago

    So cool. many questions arise.

  • Pickles The Dog
    Pickles The Dog 7 days ago +1

    4d people are drawing in 3d right now

  • Sadman Pranto
    Sadman Pranto 7 days ago

    I have self destructive personality.... This video burns my nervs but i watched at least 8 times as of now

  • Tudoricasmigal TV
    Tudoricasmigal TV 7 days ago

    Feel Better
    Minecraft Beacon is a HyperCube

  • Alexandre Moraes
    Alexandre Moraes 8 days ago

    amazing Brazilian following up

  • Mechafinch Personal
    Mechafinch Personal 8 days ago +1

    One of my greatest hopes for future technology is the ability to truly visualize 4D space and shapes

  • Cody Brown
    Cody Brown 8 days ago

    This is too much! I came home drunk, ate leftover pizza and thought dimensions were pretty cool... Now I have a polytope on order from Amazon and I need a new mind cause mines blown

  • Jorge Solar
    Jorge Solar 8 days ago

    Me encantó la traducción de youtube xd

  • A.V. X.D.
    A.V. X.D. 9 days ago

    Actually, as we, 3D creatures, see infinite polygons in 2 Dimension, a 4D creature actually sees infinite platonic solids in 3 Dimension, and we can only see 5 of them. Now think about 6D creatures and so on.

  • DogeMcMeow oof
    DogeMcMeow oof 9 days ago

    im from a diamension so high that scientists are still trying to figure out what you would consider what diamension we live in would be

  • TheSphongleface
    TheSphongleface 9 days ago

    All of this is as useless as it is man made.

  • Dave Deo
    Dave Deo 10 days ago

    2 + 2 = 3 (extra 1 popped out in 4d)

    Just kidding.. 😂

  • Dave Deo
    Dave Deo 10 days ago

    Glad you made the video.

  • George Orsa
    George Orsa 10 days ago

    That other guy sounds like maxmoefoe.

  • Alberto Antón Benítez


  • Nevezla
    Nevezla 11 days ago

    Thank you so much. very interesting

  • Nevezla
    Nevezla 11 days ago

    icosahedron has no polytope :( so sad

  • Marisa Caleche
    Marisa Caleche 11 days ago

    Niki Lauda meets Menotti

  • james bennett
    james bennett 11 days ago

    want to see in real life have some dmt case closed hahaahahaa

    • james bennett
      james bennett 11 days ago

      geometric is only a human word high doses of dmt take you to dimensions unfathomable

  • Callum Palliser-Hanks
    Callum Palliser-Hanks 11 days ago

    You lost me at 5

  • MrThat0neperson
    MrThat0neperson 12 days ago


  • J Leone
    J Leone 12 days ago

    Is there a way to purchase these models or do I need to find a 3D printer?

  • Toby Mardis
    Toby Mardis 14 days ago

    Will artificially intelligence be bound by our 3d brains? Will Brain interfacing allow us to experience higher dimensions?

  • Nate
    Nate 15 days ago

    Are there 11 other pentagons? yikes town.

  • David AE Levy
    David AE Levy 15 days ago

    With the triangles, each of those steps changes the process of closure to become the given solid. 🤔

  • Alex Works
    Alex Works 15 days ago

    Wait, aren’t those still all 3D shapes. Really want to understand other dimensions but haven’t yet understood where this other dimension comes from or how it’s measured.

    • Han Byeol Lee
      Han Byeol Lee 12 days ago

      he just show us higher dimention shapes with "3D structure"
      just like when you draw 3D cube in 2D image. it look like not rectangular in 2D but we all know it is rectangle.
      So 4D or higher structures are not looks like perfect shape because we are seeing in 3D. but it has perfect shape

  • misterjohn john
    misterjohn john 16 days ago +1


  • J David
    J David 17 days ago

    This is the best explanation of a dmt experience ever.

  • Klasoweit
    Klasoweit 17 days ago

    Maybe I missed it, but where was the 16-cell, the sixth 4D-polytope?

  • Heather Vazquez
    Heather Vazquez 17 days ago

    I would like to hear Carlo’s thoughts on the real crop circles. Please.🙏🏻

  • Jimmy David
    Jimmy David 19 days ago +1

    Is a hypercube the same thing as a tesseract?

    • ebiljebus
      ebiljebus 18 days ago +1

      A tesseract is another name for a hypercube, yes.

  • Bruno Jimmy
    Bruno Jimmy 20 days ago

    muy largo al pedo el video
    unnecesary long video

  • Bruno Jimmy
    Bruno Jimmy 20 days ago

    when the shapes appears?

  • az
    az 20 days ago

    Notice: Your brain wants to die.

  • TheFamousArthur
    TheFamousArthur 22 days ago

    Let's do some:
    3 tetrahedra 211.5 degrees
    4 tetrahedra 282 degrees
    5 tetrahedra 352.5 degrees
    6 tetrahedra 423 degrees
    3 cubes 270 degrees
    4 cubes 360 degrees
    5 cubes 450 degrees
    3 octahedra 328.5 degrees
    4 octahedra 438 degrees
    3 dodecahedra 349.5 degrees
    4 dodacehedra 466 degrees
    3 icosahedra 414 degrees

  • TheFamousArthur
    TheFamousArthur 22 days ago

    Let's do some:
    3 triangles 180 degrees
    4 triangles 240 degrees
    5 triangles 300 degrees
    6 triangles 360 degrees
    7 triangles 420 degrees
    3 squares 270 degrees
    4 squares 360 degrees
    5 squares 450 degrees
    3 pentagons 324 degrees
    4 pentagons 432 degrees
    3 hexagons 360 degrees
    4 hexagons 480 degrees
    3 heptagons 384 degrees

  • Wa Duz
    Wa Duz 23 days ago

    Klettern Sie in eine neue Dimension of Investment! ?
    Möchten Sie mit wenig Geld hohe 4 dimensionale Renditen erzielen und reich(Millionär) werden? Investieren Sie in brasilianische Tiefpreis- Grundstücke!".
    Wo suchen? Im Internet!

  • bob smith
    bob smith 23 days ago

    Are there shapes in the fourth dimension that don’t exist in the third dimension?

  • notMax Awa
    notMax Awa 23 days ago

    How would stellated polygons plook like in 4d?

  • abiram padmadhar
    abiram padmadhar 24 days ago


  • Pilot S
    Pilot S 25 days ago

    Holiey shiet, this is amazing

  • Drek Picken
    Drek Picken 25 days ago


  • Ursa Major
    Ursa Major 26 days ago +1

    Mr Sequin is the Morpheus of Geometry

  • Kelton M
    Kelton M 26 days ago

    Hey Numberphile! Where would I go to find the argument or proof of the 4th dimension in mathematics? Thank you! :)

  • Bob Jones
    Bob Jones 26 days ago

    How do they know that shapes of higher number of vertices in 2d wont make a closed shape (like decahrdron and stuff going to infinity)

  • Jonás Weimann
    Jonás Weimann 26 days ago


  • ismail hakkı yağan
    ismail hakkı yağan 26 days ago

    this is a very nice proof of FERMAT THEOREM

  • Super Awesome Fun
    Super Awesome Fun 27 days ago

    There are 10 plattonic soilds.

  • Petriell0
    Petriell0 28 days ago

    what others see : geometry
    what i see : D&D dices

    RSFAKQJ10 RSF- 28 days ago

    I am waiting for the 10D shape in the near future

  • Kavi Vaidya
    Kavi Vaidya 28 days ago

    CAL!!! My alama mater!!!

  • Richard Bull
    Richard Bull Month ago

    Better go to the gym, gotta get in better shape :)

  • Eduardo Garrido
    Eduardo Garrido Month ago

    When I die, I want that my life' story be narrated by him.

  • Johannes H
    Johannes H Month ago +2

    I'm excited for the first person growing up in 4 Dimensions, in the time when living in a simulation will be a normal thing.

  • Im.rlly. bored.
    Im.rlly. bored. Month ago

    Heres a crazy theorie. What if 4 dimensional is the astral plane. Or where ghosts are. So if souls were real, could there possibly a space for us to go.

  • Andriana Holubka
    Andriana Holubka Month ago

    Being the Japanese Language Philologist... I am enjoying this video quite a lot, thank you

  • ButterGraffion Dorito

    We see in 2d though... This blew my mind when I first found it out.

  • Luis De Pablo
    Luis De Pablo Month ago

    if any shape can exist in 2 dimensions but only 5 in 3 dimensions, how can anything exist in higher dimensions?

  • Mexican JoJo
    Mexican JoJo Month ago

    Basically, just try to point "inside" or "outside"

  • saeed kashan
    saeed kashan Month ago

    Very very easy to imagine. No problem 😄

  • Philosiraptor Jr
    Philosiraptor Jr Month ago

    6:29 Top 10 anime betrayals.

  • TheFamousArthur
    TheFamousArthur Month ago

    414 degrees /warped\

  • TheFamousArthur
    TheFamousArthur Month ago

    466 degrees /warped\

  • TheFamousArthur
    TheFamousArthur Month ago

    349.5 degrees /barely fits\

  • TheFamousArthur
    TheFamousArthur Month ago

    438 degrees /warped\

  • TheFamousArthur
    TheFamousArthur Month ago

    328.5 degrees /kind of fits\

  • TheFamousArthur
    TheFamousArthur Month ago

    450 degrees /warped\

  • TheFamousArthur
    TheFamousArthur Month ago

    360 degrees /completely filled\

  • TheFamousArthur
    TheFamousArthur Month ago

    270 degrees /fits\

  • TheFamousArthur
    TheFamousArthur Month ago

    423 degrees /warped\

  • TheFamousArthur
    TheFamousArthur Month ago

    352.5 degrees /barely fits\

  • TheFamousArthur
    TheFamousArthur Month ago

    282 degrees /fits\

  • TheFamousArthur
    TheFamousArthur Month ago

    211.5 degrees /fits\

  • TheFamousArthur
    TheFamousArthur Month ago

    Learning fractions of degrees

  • TheFamousArthur
    TheFamousArthur Month ago

    384 degrees /warped\

  • TheFamousArthur
    TheFamousArthur Month ago

    480 degrees /warped\

  • TheFamousArthur
    TheFamousArthur Month ago

    360 degrees /completely filled\

  • TheFamousArthur
    TheFamousArthur Month ago

    432 degrees /warped\

  • TheFamousArthur
    TheFamousArthur Month ago

    324 degrees /kind of fits\

  • TheFamousArthur
    TheFamousArthur Month ago

    450 degrees /warped\

  • TheFamousArthur
    TheFamousArthur Month ago

    360 degrees /completely filled\

  • TheFamousArthur
    TheFamousArthur Month ago

    270 degrees /fits\

  • TheFamousArthur
    TheFamousArthur Month ago

    420 degrees /warped\

  • TheFamousArthur
    TheFamousArthur Month ago

    360 degrees /conpletely filled\