Follow trail #4 from the Cathedral Spires parking lot towards the spires. When the trail turns left and starts uphill just before (left of) the spires, there are two options:
1) Continue uphill on the trail to the backside of the spires. As the trail enters a valley and starts to contour, look for a climber trail on the right. The climber trail begins approximately around 43° 50' 56.0364", -103° 32' 7.332" or, in decimal form, 43.848899, -103.53537. The climber trail may not be the most obvious but follows a rock path. Follow this up to a notch in the spires near the Station 13 spire. The climber trail will lead to a notch that is right at the base of Route 4 on Spire 2. From this notch, International Chimney on Spire 3 will be clearly visible up and left. In 2020, this is the approach the vast majority of climbers are doing to reach Balcony Point, Spire 2 and Spire 3.
2) Take one of the three climber trails that leave from the right side of the main trail. Wander up the slope about 200 yards to the second gully on the left, which is the gully between Spire 2 and Spire 3. Head steeply up this gully (with Rubaiyat Spire at the bottom) about 300 yards. Balcony Point and Spire 2 are at the the top of the gully on the left. The most commonly climbed route on Spire 2 is the East Face, the base of which is easily identified by a large, flat staging area. In 2020, very few people were using this approach.
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