diff --git a/src/components/Faux3DLattice.vue b/src/components/Faux3DLattice.vue
index 22be0375..cbbcad12 100644
--- a/src/components/Faux3DLattice.vue
+++ b/src/components/Faux3DLattice.vue
@@ -5,7 +5,6 @@
  */
 import { useJiLatticeStore } from '@/stores/ji-lattice'
 import { spanLattice3D } from 'ji-lattice'
-import { TimeMonzo, type Interval } from 'sonic-weave'
 import { computed, nextTick, reactive, ref, watch } from 'vue'
 
 const EPSILON = 1e-6
@@ -16,7 +15,7 @@ const NEAR_PLANE = 0.5
 const store = useJiLatticeStore()
 
 const props = defineProps<{
-  relativeIntervals: Interval[]
+  monzos: number[][]
   labels: string[]
   colors: string[]
   heldNotes: Set<number>
@@ -26,24 +25,8 @@ const svgElement = ref<SVGSVGElement | null>(null)
 
 const viewBox = reactive([-1, -1, 2, 2])
 
-const monzos = computed(() => {
-  const numComponents = store.horizontalCoordinates.length
-  const result: number[][] = []
-  for (const interval of props.relativeIntervals) {
-    const value = interval.value.clone()
-    if (value instanceof TimeMonzo) {
-      value.numberOfComponents = numComponents
-      const monzo = value.primeExponents.map((pe) => pe.valueOf())
-      result.push(monzo)
-    } else {
-      result.push(Array(numComponents).fill(0))
-    }
-  }
-  return result
-})
-
 const lattice = computed(() => {
-  const result = spanLattice3D(monzos.value, store.latticeOptions3D)
+  const result = spanLattice3D(props.monzos, store.latticeOptions3D)
   // Center everything so that the vanishing point is at the center of the view box
   const inorm = 1 / result.vertices.length
   const avgX = result.vertices.reduce((s, v) => s + v.x, 0) * inorm
@@ -72,6 +55,7 @@ watch(
     svgElement.value,
     lattice.value,
     props.labels,
+    store.depth,
     store.labelOffset,
     store.size,
     store.showLabels
diff --git a/src/components/JustIntonationLattice.vue b/src/components/JustIntonationLattice.vue
index 05750a7c..3683a545 100644
--- a/src/components/JustIntonationLattice.vue
+++ b/src/components/JustIntonationLattice.vue
@@ -19,7 +19,10 @@ const svgElement = ref<SVGSVGElement | null>(null)
 const viewBox = reactive([-1, -1, 2, 2])
 
 const monzos = computed(() => {
-  const numComponents = store.horizontalCoordinates.length
+  const numComponents = Math.max(
+    store.horizontalCoordinates.length,
+    store.verticalCoordinates.length
+  )
   const result: number[][] = []
   for (const interval of props.relativeIntervals) {
     const value = interval.value.clone()
diff --git a/src/stores/ji-lattice.ts b/src/stores/ji-lattice.ts
index f7bbf0ba..09e147cf 100644
--- a/src/stores/ji-lattice.ts
+++ b/src/stores/ji-lattice.ts
@@ -10,7 +10,7 @@ import {
   WGP9,
   primeSphere
 } from 'ji-lattice'
-import { LOG_PRIMES, mmod } from 'xen-dev-utils'
+import { LOG_PRIMES, dot, mmod } from 'xen-dev-utils'
 import { computedAndError } from '@/utils'
 import { TimeMonzo, parseChord } from 'sonic-weave'
 
@@ -209,8 +209,25 @@ export const useJiLatticeStore = defineStore('ji-lattice', () => {
   }
 
   // 3D presets
+
+  function autoDepth(monzos: number[][]) {
+    if (!xCoords.length || !yCoords.length || !zCoords.length) {
+      return
+    }
+    const x = monzos.map((m) => dot(m, xCoords))
+    const y = monzos.map((m) => dot(m, yCoords))
+    const z = monzos.map((m) => dot(m, zCoords))
+    const objectSize = Math.max(
+      Math.max(...x) - Math.min(...x),
+      Math.max(...y) - Math.min(...y),
+      Math.max(...z) - Math.min(...z)
+    )
+    depth.value = Math.ceil(2 * objectSize)
+  }
+
   function WGP(equaveIndex = 0) {
     size.value = 2
+    depth.value = 100
     const w = WGP9(equaveIndex)
     xCoords.length = 0
     xCoords.push(...w.horizontalCoordinates)
@@ -348,6 +365,7 @@ export const useJiLatticeStore = defineStore('ji-lattice', () => {
     scott24,
     pr72,
     pe72,
+    autoDepth,
     WGP,
     sphere,
     pitch,
diff --git a/src/views/LatticeView.vue b/src/views/LatticeView.vue
index 98bc075a..7d2dcaab 100644
--- a/src/views/LatticeView.vue
+++ b/src/views/LatticeView.vue
@@ -12,6 +12,7 @@ import { useGridStore } from '@/stores/grid'
 import { useCyclesStore } from '@/stores/edo-cycles'
 import { setAndReportValidity } from '@/utils'
 import Faux3DLattice from '@/components/Faux3DLattice.vue'
+import { TimeMonzo } from 'sonic-weave'
 
 const state = useStateStore()
 const scale = useScaleStore()
@@ -56,6 +57,26 @@ const heldNotes = computed(() => {
   return result
 })
 
+const monzos3D = computed(() => {
+  const numComponents = Math.max(
+    jiLattice.xCoords.length,
+    jiLattice.yCoords.length,
+    jiLattice.zCoords.length
+  )
+  const result: number[][] = []
+  for (const interval of scale.latticeIntervals) {
+    const value = interval.value.clone()
+    if (value instanceof TimeMonzo) {
+      value.numberOfComponents = numComponents
+      const monzo = value.primeExponents.map((pe) => pe.valueOf())
+      result.push(monzo)
+    } else {
+      result.push(Array(numComponents).fill(0))
+    }
+  }
+  return result
+})
+
 watch(jiPreset, (newValue) => {
   switch (newValue) {
     case 'grady':
@@ -97,14 +118,15 @@ watch(preset3D, (newValue) => {
   switch (newValue) {
     case 'WGP':
       jiLattice.WGP()
-      return
+      break
     case 'sphere':
       jiLattice.sphere()
-      return
+      break
     case 'sphere3':
       jiLattice.sphere(1)
-      return
+      break
   }
+  jiLattice.autoDepth(monzos3D.value)
 })
 
 function inferConfig() {
@@ -152,12 +174,15 @@ function inferConfig() {
     // Set the config for 3D too, but use isometric by default
     if (limit <= 9) {
       jiLattice.WGP(equaveIndex)
+      jiLattice.autoDepth(monzos3D.value)
       jiLattice.kraigGrady(equaveIndex)
     } else if (limit <= 24) {
       jiLattice.sphere(equaveIndex, 24)
+      jiLattice.autoDepth(monzos3D.value)
       jiLattice.scott24(equaveIndex)
     } else if (equaveIndex < 72) {
       jiLattice.sphere(equaveIndex, 72)
+      jiLattice.autoDepth(monzos3D.value)
       jiLattice.pe72(equaveIndex)
     } else {
       return
@@ -247,7 +272,7 @@ onMounted(() => {
       v-else-if="state.latticeType === '3d'"
       :labels="scale.latticeLabels"
       :colors="scale.latticeColors"
-      :relativeIntervals="scale.latticeIntervals"
+      :monzos="monzos3D"
       :heldNotes="heldNotes"
     />
     <template v-else>