Sure. There are all-solid ICBMs, so there are flying examples. See Minotaur, a 5-stage solid booster made from converted ICBMs. An earlier design for the Arian

Sure. There are all-solid ICBMs, so there are flying examples. See Minotaur, a 5-stage solid booster made from converted ICBMs. An earlier design for the Ariane 6 was 4 identical solid boosters, 3 on the 1st, and one for the 2nd stage--before they came to their senses. Solids are convenient and reasonably simple and good at high thrust and smaller scale, but don't scale up as well as liquids. (You try casting a fuel grain the size of an office building!) So they're not well suited for launching anything particularly large into orbit. And unfortunately they have nowhere near the mass fraction to do SSTO. Liquids, though, are tantalizingly close.