If you work it out, I would love some instructions and parts lists.
I did some research a while ago considering using a 555 timer for a different use. I couldn't really figure out how to adjust the timings and the schematics I found in any number of sites were a bit confusing. I have a basic understanding of electronics, but there are so many symbols I no longer recognize. tack on the wealth of variable components (capacitors, Inductors, timers, etc) I finally gave up as I didn't have time to start a new hobby.
one site you may find useful is www.eng-tips.com
It's a site where professional engineers gather to ask and answer questions. check out the electrical engineers forum for specific answers or to ask questions.

So far I'm having trouble getting on/off times that are that far apart. I'm sure there is a work-around but I haven't found it yet. I can go on for 2 seconds off for 3 or on for 30 minutes off for 28, but I cant get on for a couple minutes off for nearly an hour. I'm going to keep playing with it and hopefully I'll get it figured out. If/when I do I'll post a full parts list w/ Mouser part numbers (Mouser is my favorite electronics supplier) and easy-for-someone-who-isn't-an-electrical-engineer-to-read instructions.

The trouble with a 555 timer is that you need a large elco cap for long times, and elco's are notoriously inaccurate.

Best is to get a commercial mains timer that will trigger a 555 to latch for 3 minutes.

I thought I'd pass along how I intend to create a timing cycle similar to yours.
I have two intermatic timers. Each has 14 on/offs per day.
I intend to splice them in parallel through an extension chord and program each to be off 12 hours per day, then use the other 13 settings to vary the times. when one is off the other is in its programmable cycle. then 12 hours later, they trade places.
each timers runs 25-30 dollars which is hefty, but they're pretty nice.
Alternatively you could program it to turn off at 8pm, then on/off once at about 1am, then on at 6am. from 6am t0 8pm you'd have 12 cycles to work with which come to 1hour 10 minutes between cycles. this could be 10 mins on, 1 hour off or 3 minutes on, 1hour 7minutes off. this way you only need one timer per system.
the reason for the long off times from 8pm to 6am is that is the dark cycle.

sdrawkcab, The best way would be to use the 555 to control the relatively short "on" time. To get the long "off" time, use a combination oscillator/divider (or counter) chip. The oscillator/divider part could put out a continuous pulse that has an "on" time equal to the "off" time, at a rate of lets say one long "cycle" every 60 minutes (easily obtainable). That could feed the 555 so that the negative going edge (once an hour in this case) triggers the 555 in "one-shot" mode to produce a 3 minute pulse. John

Shouldn't be rocket science for some person with the right skill set to get a plan and part list from this or any other (corresponding) kit? No need to even dismantle it, I guess.

This one is said to be adjustable from about 45 seconds to 60 minutes
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Universal Start/Stop Timer - Kit or Assembled Circuit
This kit is a timer with unlimited applications. It is adjustable from about 45 seconds to 60 minutes. It includes a relay which can handle loads of up to 3A / 110V AC or 24V DC and Start/Stop push button switches. The time interval is set through a PCB mounted variable resistor.

Specifications:

Supply voltage: 12V DC or 9V AC Transformer / 100mA
Time adjustable from 45 seconds to 60 minutes
Output Relay:
UNIVERSAL STOP/START TIMER
Maximum 3A at 110V AC or 24V DC
Maximum 1.5A at 220V AC
PC board dimensions: 3.13" x 1.48"
See all our timers by clicking here ->

Note: If you choose the kit form, you will receive parts to build the item pictured. If you do not know how to solder you can check out our learn to solder kit. CANCK158 - Universal Start/Stop Timer (Kit) - $15.95 CANUK158 - Universal Start/Stop Timer (Assembled) - $18.95
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Here is a link that might be useful: Source

Lucas, that looks like a timer that gives you an output, picking the relay for, as you stated, 45 seconds to 60 minutes EVERY TIME YOU PUSH THE BUTTON. I believe the original poster was looking for roughly 3 minutes on and 1 hour off for as long as the device was turned on.

Not sure about if you actually need to push any button to start the timer, I more think those TWO buttons are in fact to set the timer (digital display included?). But I may be wrong. Anyway the purpose here was to give a hint for a way to go: buy a kit (that FITS your needs as I stated) and draw a plan from what you have in hands and a part list as well - actually copy the whole thing for others.

The best way to do this isn't to use a single 555 timer to control everything. Better case would be to use a micro-controller that's cheap, like a PIC, a short timer, say 20ms, and a few overflow counters. It'd be trivial to code. But not everyone has a PIC programmer like I do sitting here.

I would be interested in a cheap (parts) and flexible timer plan as well, in fact to use with a high pressure pump system for a vertical frame setup for micro greens as seen on YouTube vids. I would have some student build those for me as I haven't the skill- nor toolset for it. But I'd of course prefer (actually only be interested in) a STAND ALONE unit that is easy to set and use as well.

Homebrew cycle timers are fairly straightforward to make if you have basic soldering skills. They are no less reliable than the more expensive store bought timers.
As well as the cost benefits,12vdc operation means power outages don`t affect them. In fact, they can run completely off-grid using a battery and a solar panel for trickle charging.

Radio shack has a beginners book of electric hobbist project that have 555 computer chips that you can set up any way you want. Give them a call, they even have circut boards already made for plug and play. And yes their cheap. I still have one of the books in storage I may check out just for old times.

I haven't toyed with electronics since I retired my 1/8 scale radio controlled hydroplanes about 25 years ago but I remember the radio shack books georgeiii is talking about. I never had much use for the 555/556 timers in those days, But I can see where they would be quite applicable to a cycling timer for a hydroponic system. So I did a search, try this; www.orchidboard.com/community/terrarium-gardening/3656-timer-question-2.html