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National Boards => General Highway Talk => Topic started by: hotdogPi on March 17, 2022, 11:00:33 AM

Title: Are there any Penrose loops within an interchange?
Post by: hotdogPi on March 17, 2022, 11:00:33 AM
(Penrose loop isn't an established term, but I'm calling it that in analogy with Penrose stairs.)

Three or more overpasses/underpasses. Road A goes over Road B. Road B goes over Road C. Road C goes over Road A, or if there are more than three, it forms a cycle analogously. Connections (or lack thereof) between the road don't matter. Railroads are allowed, and this thread is not limited to the United States.
Title: Re: Are there any Penrose loops within an interchange?
Post by: froggie on March 17, 2022, 11:21:45 AM
Though it's not a single interchange, would you classify I-495/VA 7/VA 123 at Tysons Corner as such?
Title: Re: Are there any Penrose loops within an interchange?
Post by: hotdogPi on March 17, 2022, 11:26:28 AM
Quote from: froggie on March 17, 2022, 11:21:45 AM
Though it's not a single interchange, would you classify I-495/VA 7/VA 123 at Tysons Corner as such?

It definitely meets the criteria that no single road is on top.
Title: Re: Are there any Penrose loops within an interchange?
Post by: CardInLex on March 17, 2022, 12:00:11 PM
In Louisville, traffic going from I-65 NB to I-64 EB does quite a few ups and downs:
1) Goes under the C/D ramp to I-65 NB
2) Goes over I-71
3) Then immediately, goes under the same I-71 traffic they just went over

Conversely, I-65 NB to I-71 NB traffic:
1) Goes under the C/D ramp to I-65 NB
2) Goes under I-64
3) Then immediately, goes over the same I-64 traffic they just went under

https://goo.gl/maps/ERbaVhXBzJW36DBi6

Both also pass under on ramps to their respective directions and go over a local street/railroad.
Title: Re: Are there any Penrose loops within an interchange?
Post by: hotdogPi on March 17, 2022, 12:10:37 PM
Quote from: CardInLex on March 17, 2022, 12:00:11 PM
In Louisville, traffic going from I-65 NB to I-64 EB does quite a few ups and downs:
1) Goes under the C/D ramp to I-65 NB
2) Goes over I-71
3) Then immediately, goes under the same I-71 traffic they just went over

Conversely, I-65 NB to I-71 NB traffic:
1) Goes under the C/D ramp to I-65 NB
2) Goes under I-64
3) Then immediately, goes over the same I-64 traffic they just went under

https://goo.gl/maps/ERbaVhXBzJW36DBi6

Both also pass under on ramps to their respective directions and go over a local street/railroad.

I-65 plus one of its southbound exit ramps is on top, and there are two ramps that would be on top if not for I-65. Unless the loop is entirely below those ramps, it doesn't seem to qualify.
Title: Re: Are there any Penrose loops within an interchange?
Post by: webny99 on March 17, 2022, 12:17:44 PM
Quote from: 1 on March 17, 2022, 11:26:28 AM
Quote from: froggie on March 17, 2022, 11:21:45 AM
Though it's not a single interchange, would you classify I-495/VA 7/VA 123 at Tysons Corner as such?

It definitely meets the criteria that no single road is on top.

I'm looking at that as a baseline, and then seeing if I can find examples with a smaller triangle.
Title: Re: Are there any Penrose loops within an interchange?
Post by: webny99 on March 17, 2022, 12:30:44 PM
I found a slightly smaller one in Amherst, NY: https://www.google.com/maps/@42.9883929,-78.7919831,16.25z

I-290 > NY 263 > Maple Rd > I-290 with a perimeter distance of about 1.5 miles vs. about 2.5 miles in the VA example.
Title: Re: Are there any Penrose loops within an interchange?
Post by: jmacswimmer on March 17, 2022, 12:41:42 PM
Breezewood, PA: (https://www.google.com/maps/@39.9884843,-78.2464849,1399m/data=!3m1!1e3!5m1!1e1?hl=en)

-I-76/PA Turnpike mainline passes under I-70/PA Turnpike ramp & over Free I-70
-I-70/PA Turnpike ramp passes over I-76/PA Turnpike mainline & under Free I-70
-Free I-70 passes over I-70/PA Turnpike ramp & under I-76/PA Turnpike mainline

Perimeter of ~1.85 miles.
Title: Re: Are there any Penrose loops within an interchange?
Post by: GaryV on March 17, 2022, 01:46:25 PM
I don't know what "Penrose" means, but would the US-131/I-196 interchange in Grand Rapids qualify?

I-196 eb goes under everything; I-196 wb goes over everything. US-131 sb crosses over US-131 nb, and then crosses back under it. (Like a DDI, but with overpasses.)
Title: Re: Are there any Penrose loops within an interchange?
Post by: hotdogPi on March 17, 2022, 02:12:15 PM
Quote from: GaryV on March 17, 2022, 01:46:25 PM
I don't know what "Penrose" means

https://en.wikipedia.org/wiki/Penrose_stairs

I couldn't think of a better term.
Title: Re: Are there any Penrose loops within an interchange?
Post by: jmacswimmer on March 17, 2022, 02:22:43 PM
Alright, I think I found an example that is actually one single interchange rather than the larger "interchange systems" posted so far:

I-97/MD 3/MD 32 in Millersville MD. (https://www.google.com/maps/@39.0650698,-76.639336,1032m/data=!3m1!1e3?hl=en)
Title: Re: Are there any Penrose loops within an interchange?
Post by: CtrlAltDel on March 17, 2022, 03:53:44 PM
It's not what you had in mind, but when I-5 crosses itself north of Castaic CA, the southbound lanes pass over the northbound lanes, but when they uncross themselves further north, the northbound lanes pass over the southbound lanes.