Penrose staircase

Higher-dimensional geometry (previously "Polyshapes").

Penrose staircase

Postby Marek14 » Thu Oct 10, 2019 7:34 pm

With Hyper Rogue's recent implementation of anisotropic Thurston geometries, one interesting note is that the Nil geometry (twisted Euclidean geometry) actually includes well-known "impossible structures" like Penrose triangles and staircases as solid, real objects. Was that known?
Marek14
Pentonian
 
Posts: 1191
Joined: Sat Jul 16, 2005 6:40 pm

Re: Penrose staircase

Postby mr_e_man » Mon Dec 02, 2019 8:30 pm

Ugh. :x Someone vandalized the Penrose tribar page. (See "tribal", "pen rose", "Pennose", "thermal", and "cows" in an earlier edit.)

But it did say "Such an object can exist in certain Euclidean 3-manifolds".
ΓΔΘΛΞΠΣΦΨΩ αβγδεζηθϑικλμνξοπρϱσςτυϕφχψωϖ °±∓½⅓⅔¼¾×÷†‡• ⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎
ℕℤℚℝℂ∂¬∀∃∅∆∇∈∉∋∌∏∑ ∗∘∙√∛∜∝∞∧∨∩∪∫≅≈≟≠≡≤≥⊂⊃⊆⊇ ⊕⊖⊗⊘⊙⌈⌉⌊⌋⌜⌝⌞⌟〈〉⟨⟩
mr_e_man
Tetronian
 
Posts: 474
Joined: Tue Sep 18, 2018 4:10 am


Return to Other Geometry

Who is online

Users browsing this forum: No registered users and 6 guests