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On Earth, life took on a quadruped body plan which has lead to many different sub body plans; 4 legged, 2 legs-2 wings, 2 legs-2 arms, etc. This has made me wonder what possible sub body plans can exist on hexapods. Ignoring tails, what are the possible ways a hexapods limbs can be arranged?

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    $\begingroup$ are these creatures radially symmetrical or bi-lateral? or even tri-lateral? $\endgroup$ – XenoDwarf Jul 18 '16 at 23:09
  • $\begingroup$ @TunaDragon As they are aliens, I'm going to say that they could be any of the three $\endgroup$ – TrEs-2b Jul 18 '16 at 23:15
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    $\begingroup$ I might point out all bugs, snakes, and a moa bird. Just because not everything is a quadruped. $\endgroup$ – Xandar The Zenon Aug 6 '16 at 23:11
  • $\begingroup$ @XandarTheZenon And starfish. They might not be hexapod, but you can certainly imagine them being so fairly easily. $\endgroup$ – DKNguyen Aug 13 '20 at 2:45
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Wings, I suppose, only work in pairs, so they must be an even number (and imply bilateral symmetry): 2, 4, or 6, or, of course, none.

Legs seem to be necessarily more than one, or none.

Arms could be any number, from 0 to 6, though 5 would be weird, as wings need to be in even numbers, and legs need to be more than one.

Fins could be in any number, but their relation to symmetry is interesting; I suppose they could be radially distributed in a perpendicular plan to an otherwise bilateral organism.

So, ignoring other possible - or impossible, but interesting - kinds of members...

  • 6 wings disposed in three pairs - weird creature that only flies. I doubt this could be a predator, unless it has a bucal apparatus like those of ants.

  • 4 wings and two legs - bilateral creature with as many legs as a bird, and as many wings as an insect.

  • 2 wings and 4 legs - Pegasus!

  • 4 wings and 2 arms - they must fly to move, or crawl on their arms. But then are their arms really arms?

  • 2 wings and 4 arms - same as above. Somehow, I feel that with time two of these arms would evolve into legs unless they live in places with extremely irregular relief.

  • 4 wings and 2 fins - similar to some flying fish?

  • 2 wings and 4 fins - another kind of flying acquatic animal.

  • 6 legs - could have either a radial or a bilateral distribution (like a wingless insect, Lepisma for instance).

  • 5 legs and 1 arm - like a starfish with an arm at its centre...

  • 4 legs and 2 arms - Centauri!

  • 3 legs and 3 arms - another radial monster.

  • 2 legs and 4 arms - I think some creatures in the movie Men in Black are like this. Also, similar to some Hindu gods, though with less arms.

  • 6 arms - a fixed animal, perhaps, like some sea anemones with hands at the end of their tentacles. Or maybe like an octopus with two tentacles less - but are they still arms if their primary use is locomotion?

  • 5 arms and 1 fin - a radial creature, probably a seagoing predator.

  • 4 arms and 2 fins - like a dolphin with arms? Or mermaids with extra arms?

  • 3 arms and 3 fins - a quite weird radial critter.

  • 2 arms and 4 fins - Mermaids? Fins could be distributed either bilaterally or radially.

  • 1 arm and 5 fins - perhaps like an anglerfish with an actual arm instead of an illicium?

  • 6 fins - very much like a dolphin with two extra fins. Or could be like some creatures in Escher etchings, also with two more fins.

  • 2 wings, 2 legs, 2 arms - Angels, for instance.

  • 2 wings, 3 legs, 1 arm - a small change, and they don't like angels at all anymore.

  • 2 wings, 3 legs, 1 fin - not sure that such critter would be able to either fly, walk, or swim.

  • 2 wings, 2 legs, 2 fins - winged tadpoles?

  • 4 wings, 1 arm, 1 fin - again, not sure this could function.

  • 4 legs, 1 arm, 1 fin - like a starfish with an arm and a fin, and a leg less?

  • 2 legs, 2 arms, 2 fins - Mermaids with legs?

  • 2 legs, 3 arms, 1 fin - another monster I have trouble visualising.

  • 3 legs, 2 arms, 1 fin - I shouldn't be writing this at night, it might give me nightmares.

  • 3 legs, 1 arm, 2 fins - and this is hardly better... I can only hope they don't have mouths like those of lampreys.

    and finally,

  • 2 wings, 2 legs, 1 arm, 1 fin - I wonder what environment would have produced this kind of thing. Semi-submersed forests, perhaps?

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  • $\begingroup$ Beautifully done! +1 $\endgroup$ – TrEs-2b Jul 19 '16 at 4:59
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    $\begingroup$ why do you need more than one leg? hopping around on one thick leg might well be doable... ;) $\endgroup$ – Syndic Jul 19 '16 at 8:02
  • $\begingroup$ @Syndic - but then it would not be a leg, it would be a hopper. And as such, it would fall into the "possible, or impossible but interesting, kinds of members" category... $\endgroup$ – Luís Henrique Jul 21 '16 at 16:08
  • $\begingroup$ Many creatures, such as bats and pterosaurs, use their wings as legs $\endgroup$ – Ichthys King May 14 '20 at 9:39
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The number of paired-limb [bilaterally symmetric] plans for hexapods will depend upon how many types of limbs one allows for; radially symmetric plans require a single limb type (otherwise, they would necessarily not be radially symmetric). Given that we're considering hexapods' hypothetical configurations, a trilateral symmetry would probably be in keeping as well.

If we assume only the constraints of your example set of {leg, wing, arm}, then the resulting possible combinations are:

  • 3 radially symmetric configurations -- legs x6, arms x6 [I would presume tentacles, here], wings x6;

  • 7 unique-counts of bilaterally symmetric combinations (not including the radially symmetric configurations, which technically qualify as any higher order of body symmetry) -- short-handed here as {a, l, w} for brevity yields {lla, llw, aal, aaw, wwa, wwl, alw};

  • 24 permutations possible, of the above-named combinations -- {arms, legs, wings} short-handed here as {a, l, w} for brevity yields {aal, aaw, all, ala, alw, awa, awl, aww, laa, lal, law, lla, llw, lwa, lwl, lww, waa, wal, waw, wll, wla, wlw, wwa, wwl}, which gives us 18 sets of two-same/one-different and 6 sets of three-different-pairs;

  • 3 trilaterally symmetric configurations, wherein the hexapods have triplets of limbs (rather than pairs), would yield alternating pairs of opposites {alalal, awawaw, lwlwlw}, not including a pair of triplets being equivalent to a bilaterally symmetric configuration (e.g.: lllwww).

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    $\begingroup$ i knew I'd regret commenting instead of answering, +1 from me $\endgroup$ – XenoDwarf Jul 18 '16 at 23:38
  • $\begingroup$ (Thank you for +1.) I saw your comment to O.P. just now, so if it's any consolation, I didn't crib notes from it. (Unfortunately, that might make it worse, since means that there might have been time enough to get in an answer of that sort before mine.) $\endgroup$ – Charles Rockafellor Jul 18 '16 at 23:40
  • $\begingroup$ I didn't mean to imply you 'cribbed notes', I was just saying we had the same idea. It's all good. $\endgroup$ – XenoDwarf Jul 18 '16 at 23:48
  • $\begingroup$ No problem; my bad on the phrasing there. I hadn't thought that that was your inference, much less implication -- I had meant only to assuage possible doubts. (I'm fumbling this badly, sorry.) $\endgroup$ – Charles Rockafellor Jul 18 '16 at 23:52
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    $\begingroup$ all is well then, good luck with the answer $\endgroup$ – XenoDwarf Jul 18 '16 at 23:55
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Two on each axis around a sphere.

One on each face of a cube.

Rather than different function but arranged in a line, they are facing or working in different directions.

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The configurations that come to mind are:

  1. 2 each for the various functions - locomotion (legs), dexterity (hands/arms), flight (wings).

  2. Radial - like a six side start fish.

  3. 3 legs, (like a tripod) and 3 arms/hands.

  4. Modification of #1: 2 each for the various functions - locomotion (legs), dexterity (hands/arms), 2 for grosser function like lifting heavy weights.

Hope that's helpful.

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Assuming that these aliens are more-or-less like vertebrates, then there are around 150 combinations:

  • arm, arm, leg: A 4-armed humanoid
  • arm, arm, fin: A 4-armed creature like a swimming crab
  • arm, arm, prehensile foot: A 4-armed ape-like creature
  • arm, arm, prehensile fin: A 6-armed creature like a swimming crab
  • arm, arm, flipper-leg: A 4-armed mermaid-like creature
  • arm, leg, leg: A centaur
  • arm, leg, prehensile foot: An ape-like centaur
  • arm, leg, flipper-leg: A mermaid-like centaur
  • arm, wing, leg: A winged humanoid
  • arm, wing, fin: A flying creature like a swimming crab
  • arm, wing, prehensile foot: A winged ape-like creature
  • arm, wing, prehensile fin: An aquiline creature like a swimming crab
  • arm, wing, flipper-leg: A winged mermaid-like creature
  • arm, fin, fin: A mermaid
  • arm, fin, flipper-leg: A mermaid with legs
  • arm, prehensile foot, prehensile foot: Another ape-like centaur
  • arm, prehensile foot, flipper-leg: An ape-like aquatic centaur
  • arm, prehensile wing, leg: A 4-armed winged humanoid
  • arm, prehensile wing, fin: A 4-armed winged creature like a swimming crab
  • arm, prehensile wing, prehensile foot: Another winged ape-like creature
  • arm, prehensile wing, prehensile fin: A 6-armed flying creature like a swimming crab
  • arm, prehensile wing, flipper-leg: An amphibous winged humanoid
  • arm, prehensile fin, prehensile fin: A sea-turtle centaur
  • arm, wing-leg, leg: A bat centaur
  • arm, wing-leg, prehensile foot: An ape-bat centaur
  • arm, wing-leg, flipper-leg: An amphibious bat-centaur
  • arm, flipper-leg, flipper-leg: Another sea-turtle centaur
  • arm, flipper-wing, fin: A flying sea-turtle centaur
  • arm, flipper-wing, flipper-leg: Another amphibious bat-centaur
  • leg, leg, leg: An insectoid
  • leg, leg, prehensile foot: An eagle-footed insectoid
  • leg, leg, flipper-leg: An amphibious insectoid
  • leg, wing, leg: A dragon
  • leg, wing, prehensile foot: An eagle-footed dragon
  • leg, wing, flipper-leg: An amphibious dragon
  • leg, fin, flipper-leg: A sea-dragon
  • leg, wing-leg, leg: A more realistic dragon
  • leg, wing-leg, prehensile foot: A realistic eagle-footed dragon
  • leg, wing-leg, flipper-leg: A realistic amphibious dragon
  • leg, flipper-leg, flipper-leg: Another amphibious insectoid
  • leg, flipper-wing, flipper-leg: Another amphibious dragon
  • wing, leg, leg: An avian quadruped
  • wing, leg, prehensile foot: An aquiline quadruped
  • wing, leg, flipper-leg: An amphibious avian quadruped
  • wing, wing, leg: A 4-winged avian creature
  • wing, wing, fin: A fully aquatic 4-winged duck-like creature
  • wing, wing, prehensile foot: A 4-winged aquiline creature
  • wing, wing, prehensile fin: A 4-winged aquiline duck-like creature
  • wing, wing, wing-leg: A 6-winged tetrapteryx
  • wing, wing, flipper-leg: An amphibious 4-winged avian creature
  • wing, wing, flipper-wing: A duck-like tetrapteryx
  • wing, fin, fin: A fully-aquatic duck-like quadruped
  • wing, fin, prehensile fin: A fully-aquatic aquiline duck-like quadruped
  • wing, fin, flipper-leg: A duck-like humanoid
  • wing, wing-leg, wing-leg: A 6-winged avian quadruped
  • wing, wing-leg, flipper-leg: A 4-winged amphibious avian quadruped
  • wing, flipper-leg, flipper-leg: A duck-like quadruped
  • wing, flipper-wing, flipper-wing: A flying fish
  • fin, fin, fin: A 6-finned fish
  • fin, fin, prehensile fin: An aquiline 6-finned fish
  • fin, fin, flipper-leg: A 6-finned humanoid fish
  • fin, flipper-leg, flipper-leg: An avian quadrupedal fish
  • fin, flipper-wing, fin: Another flying fish
  • fin, flipper-wing, prehensile fin: An aquiline flying fish
  • fin, flipper-wing, flipper-leg: A winged humanoid fish
  • prehensile foot, leg, leg: An onocentaur
  • prehensile foot, leg, prehensile foot: An ape-like onocentaur
  • prehensile foot, leg, flipper-leg: An amphibious onocentaur
  • prehensile foot, wing, leg: Another dragon
  • prehensile foot, wing, prehensile foot: An ape-like dragon
  • prehensile foot, wing, flipper-leg: Another amphibious dragon
  • prehensile foot, fin, flipper-leg: Another sea-dragon
  • prehensile foot, prehensile foot, leg: A hexapedal ape-like creature
  • prehensile foot, prehensile foot, prehensile foot: Another hexapedal ape-like creature
  • prehensile foot, prehensile foot, flipper-leg: An amphibious ape-like creature
  • prehensile foot, prehensile wing, leg: A 4-armed dragon
  • prehensile foot, prehensile wing, prehensile foot: A 6-armed dragon
  • prehensile foot, prehensile wing, flipper-leg: A 4-armed amphibious dragon
  • prehensile foot, wing-leg, leg: Another more realistic dragon
  • prehensile foot, wing-leg, prehensile foot: An ape-like realistic dragon
  • prehensile foot, wing-leg, flipper-leg: An amphibious realistic dragon
  • prehensile foot, flipper-leg, flipper-leg: A sea-turtle onocentaur
  • prehensile foot, flipper-wing, flipper-leg: A flying sea-turtle onocentaur
  • prehensile wing, arm, leg: Another 4-armed winged humanoid
  • prehensile wing, arm, fin: A 4-armed winged creature like a swimming crab
  • prehensile wing, arm, prehensile foot: A 4-armed winged ape-like creature
  • prehensile wing, arm, prehensile fin: A 4-armed aquiline creature like a swimming crab
  • prehensile wing, arm, flipper-leg: An amphibious 4-armed winged humanoid
  • prehensile wing, leg, leg: An avian quadruped with hands
  • prehensile wing, leg, prehensile foot: An aquiline quadruped with hands
  • prehensile wing, leg, flipper-leg: An amphibious avian quadruped with hands
  • prehensile wing, wing, leg: A 4-winged avian creature with hands.
  • prehensile wing, wing, fin: A fully aquatic 4-winged duck-like creature with hands
  • prehensile wing, wing, wing-leg: A 6-winged tetrapteryx with hands
  • prehensile wing, wing, flipper-leg: An 4-winged amphibious avian creature with hands
  • prehensile wing, wing, flipper-wing: A duck-like tetrapteryx with hands
  • prehensile wing, fin, fin: A fully aquatic duck-like quadruped with hands
  • prehensile wing, fin, flipper-leg: A duck-like humanoid with hands
  • prehensile wing, prehensile foot, leg: An ape-like avian quadruped
  • prehensile wing, prehensile foot, prehensile foot: Another ape-like avian quadruped
  • prehensile wing, prehensile foot, flipper-leg: An ape-like amphibious avian quadruped
  • prehensile wing, prehensile wing, leg: A 4-winged avian creature with 4 hands
  • prehensile wing, prehensile wing, fin: A fully aquatic 4-winged duck-like creature with 4 hands
  • prehensile wing, prehensile wing, prehensile foot: A 4-winged aquiline creature with 4 hands
  • prehensile wing, prehensile wing, prehensile fin: A fully aquatic 4-winged aquiline duck-like creature with 4 hands
  • prehensile wing, prehensile wing, wing-leg: A 6-winged tetrapteryx with 4 hands
  • prehensile wing, prehensile wing, flipper-leg: An amphibious avian creature with 4 hands
  • prehensile wing, prehensile wing, flipper-wing: A duck-like tetrapteryx with 4 hands
  • prehensile wing, prehensile fin, prehensile fin: A 6-armed flying fish
  • prehensile wing, wing-leg, leg: A 4-winged dragon with arms
  • prehensile wing, wing-leg, wing-leg: A 6-winged dragon with arms
  • prehensile wing, wing-leg, flipper-leg: A 4-winged amphibious dragon with arms
  • prehensile wing, flipper-leg, flipper-leg: A sea-dragon with arms
  • prehensile wing, flipper-wing, flipper-wing: A flying fish with arms
  • prehensile fin, fin, fin: A 6-finned fish with arms
  • prehensile fin, fin, prehensile fin: A 6-finned aquiline fish with arms
  • prehensile fin, fin, flipper-leg: A humanoid fish
  • prehensile fin, prehensile fin, fin: A 4-armed fish
  • prehensile fin, prehensile fin, prehensile fin: A 6-armed fish
  • prehensile fin, prehensile fin, flipper-leg: A 4-armed humanoid fish
  • prehensile fin, flipper-leg, flipper-leg: An ichthyocentaur
  • prehensile fin, flipper-wing, fin: Another flying fish with arms
  • prehensile fin, flipper-wing, prehensile fin: An aquiline flying fish with arms
  • prehensile fin, flipper-wing, flipper-leg: Another winged humanoid fish
  • wing-leg, leg, leg: A 6-legged bat-like creature
  • wing-leg, leg, prehensile foot: An aquiline 6-legged bat-like creature
  • wing-leg, leg, flipper-leg: An 6-legged amphibious bat-like creature
  • wing-leg, fin, flipper-leg: An aquatic bat-like creature
  • wing-leg, wing-leg, leg: A 4-winged bat-like creature
  • wing-leg, wing-leg, prehensile foot: A 4-winged aquiline bat-like creature
  • wing-leg, wing-leg, wing-leg: A 6-winged bat-like creature
  • wing-leg, wing-leg, flipper-leg: An amphibious 4-winged bat-like creature
  • wing-leg, flipper-leg, flipper-leg: Another amphibious 4-winged bat-like creature
  • flipper-leg, fin, flipper-leg: Another sea-dragon
  • flipper-leg, flipper-leg, flipper-leg: An aquatic insectoid
  • flipper-leg, flipper-wing, flipper-leg: Another sea-dragon
  • flipper-wing, fin, fin: Another flying fish
  • flipper-wing, fin, prehensile fin: Another aquiline flying fish
  • flipper-wing, fin, flipper-leg: Another winged humanoid fish
  • flipper-wing, flipper-leg, flipper-leg: An avian quadruped fish
  • flipper-wing, flipper-wing, fin: Another flying fish
  • flipper-wing, flipper-wing, prehensile fin: Another aquiline flying fish
  • flipper-wing, flipper-wing, flipper-leg: Another flying fish
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